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Nucl. Phys. B 228, 552–566 (1983)\nAnderson, D.: Variational approach to nonlinear pulse propagation in optical fibers. Phys. Rev. A 27, 3125–3145 (1983)\nBathe, K.: Finite Element Procedures, 2nd edn. Klaus-Jurgen Bathe, Berlin (2014)\nChristiansen, P.L., Olsen, O.H.: Ring-shaped quasi-soliton solutions to the two- and three-dimensional sine-gordon equation. Phys. Scr. 20, 531–538 (1979)\nWolfram Research, Inc. Mathematica, Version 12.2. Champaign, IL, (2020)\nKath, W.L., Smyth, N.F.: Soliton evolution and radiation loss for the nonlinear schrödinger equation. Phys. Rev. E 51, 1484–1492 (1995)\nKivshar, Y.S., Malomed, B.A.: Dynamics of solitons in nearly integrable systems. Rev. Mod. Phys. 61(4), 763 (1989)\nKudryavtsev, A., Piette, B., Zakrzewski, W.J.: Mesons, baryons and waves in the baby skyrmion model. Euro. Phys. J. C 1, 333–341 (1998)\nLamb, G.L.: Elements of Soliton Theory. Wiley, New York (1980)\nLe, K.C., Nguyen, L.T.K.: Slope modulation of ring waves governed by two-dimensional sine-gordon equation. Wave Motion 55, 84–88 (2015). (6)\nLe, K.C., Nguyen, L.T.K.: Slope modulation of waves governed by sine-gordon equation. Commun. Nonlinear Sci. Numer. Simul. 18, 1563–1567 (2013)\nMalomed, B.: Variational methods in nonlinear fiber optics and related fields. Prog. Opt. 43, 71–193 (2002)\nMcLaughlin, D.W., Scott, A.C.: Perturbation analysis of fluxon dynamics. Phys. Rev. A 18(4), 1652 (1978)\nMinzoni, A.A., Smyth, N.F., Worthy, A.L.: Evolution of two dimensional standing and travelling breather solutions for the sine-gordon equation. Physica D 189, 167–187 (2004)\nMinzoni, A.A., Smyth, N.F., Worthy, A.L.: Pulse evolution for a two-dimensional sine-gordon equation. Physica D: Nonlinear Phenomena 159, 101–123 (2001)\nNeu, J.C.: Kinks and the minimal surface equation in minkowski space. Physica D 43, 421–434 (1990)\nNguyen, L.T.K.: A numerical scheme and some theoretical aspects for the cylindrically and spherically symmetric sine-gordon equations. Commun. Nonlinear Sci. Numer. Simul. 36, 402–418 (2016)\nPiette, B., Zakrzewski, W.J.: Metastable stationary solutions of the radial \\(d\\)-dimensional sine-gordon model. Nonlinearity 11, 1103–1110 (1998)\nSamuelsen, M.R.: Approximate rotationally symmetric solutions to the sine-gordon equation. Phys. Lett. A 74, 21–22 (1979). (10)\nSmyth, N.F., Worthy, A.L.: Soliton evolution and radiation loss for the sine-gordon equation. Phys. Rev. E 60, 2330–2336 (1999)\nWhitham, G.B.: A general approach to linear and non-linear dispersive waves using a lagrangian. J. Fluid Mech. 22, 273–283 (1965)\nWhitham, G.B.: Linear and Nonlinear Waves. Wiley, New York (1974)",{"EN":155},"We derive a modulation theory for the resolution of radially symmetric kink waves governed by a multi-dimensional sine-Gordon equation. Whitham modulation theory is developed to explain the return of an expanding kink wave, as well as predicting its maximum expansion radius and its return time. Comparisons with full numerical solutions of the sine-Gordon equation show that the modulation theory gives excellent predictions for not only the returning time and the maximum expansion radius, but also for the details of the kink itself. In addition, the method can be extended to dissipative sine-Gordon equations and generalized to deal with a wide class of initial conditions beyond kinks.\n",{"EN":157},"Modulation Theory for Radially Symmetric Kink Waves Governed by a Multi-Dimensional Sine-Gordon Equation",{"VOID":159},"10.1007\u002Fs00332-022-09859-w","PUBLICATION","VERIFIED","Auto 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Nguyen","ARTICLE",{"url":163,"publisher":212,"properties":241},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":213,"slug":10,"properties":214,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":219,"manageAffiliations":220,"indexDatabases":221,"url":22,"thumbnailPath":22,"statistic":236,"gsStatistic":22,"type":140,"analyzePriority":22},[],{"issn":215,"eissn":216,"title":217,"url":218},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},[],[],[222,229],{"id":95,"indexDatabase":223,"url":108,"indexYears":109,"academicFieldIds":228,"indexDatabaseRanking":114},{"id":97,"createTime":98,"updateTime":99,"relativeEntities":224,"label":225,"description":226,"key":105,"publicationTags":227,"standard":22},[],{"EN":102,"VI":102},{"EN":102,"VI":104},[107],[111,112,113],{"id":74,"indexDatabase":230,"url":89,"indexYears":22,"academicFieldIds":235,"indexDatabaseRanking":22},{"id":76,"createTime":77,"updateTime":78,"relativeEntities":231,"label":232,"description":233,"key":85,"publicationTags":234,"standard":22},[],{"EN":81,"VI":81},{"VI":83,"EN":84},[87,88],[91,92,93],{"impactFactor":23,"impactFactorByYear":237,"i10Index":23,"i10IndexLast5Year":23,"totalPublication":117,"totalPublicationByYear":238,"totalCitation":23,"totalCitationByYear":239,"totalCitationPerPublication":23,"totalCitationPerPublicationByYear":240,"hindexLast5Year":23,"hindex":23},{},{"1991":69,"1992":119,"1993":120,"1994":121,"1995":122,"1996":123,"1997":124,"1998":122,"1999":122,"2000":125,"2001":126,"2002":69,"2003":120,"2004":122,"2005":125,"2006":69,"2007":127,"2008":123,"2009":120,"2010":121,"2011":122,"2012":128,"2013":127,"2014":129,"2015":130,"2016":131,"2017":132,"2018":131,"2019":133,"2020":134,"2021":135,"2022":136,"2023":137,"2024":123},{},{},{"volume":242,"pages":244},{"VOID":243},"33",{"VOID":245},"1-25","2022-11-19",2022,false,{"id":250,"createTime":251,"updateTime":252,"relativeEntities":253,"slug":254,"properties":255,"entityType":160,"verifyStatus":161,"verifyTime":252,"verifyNote":162,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":264,"fullTextUrl":22,"authors":265,"publicationType":210,"publisherRelationship":296,"citationCount":22,"citationInfo":22,"publishDate":330,"publishYear":331,"citationAnalyzeStatus":21,"lastCitationAnalyze":22,"indexDatabases":22,"openAccess":22,"references":22,"isForceReanalyzing":248},"0c2276c9-9578-47f0-88c5-57f4633b9a8c","2024-02-18T15:44:40.560+00:00","2024-12-14T23:52:23.615+00:00",[],"Stability-of-Heteroclinic-Cycles-A-New-Approach-Based-on-a-Replicator-Equation",{"references":256,"abstract":258,"title":260,"doi":262},{"VOID":257},"Afraimovich, V.S., Moses, G., Young, T.: Two-dimensional heteroclinic attractor in the generalized Lotka–Volterra system. Nonlinearity 29(5), 1645 (2016)\nAguiar, M.A.D.: Is there switching for replicator dynamics and bimatrix games? Physica D 240(18), 1475–1488 (2011)\nAguiar, M.A.D., Labouriau, I.S., Rodrigues, A.A.P.: Switching near a network of rotating nodes. Dyn. Syst. 25(1), 75–95 (2010)\nAlishah, H.N., Duarte, P.: Hamiltonian evolutionary games. J. Dyn. Games 2(1), 33 (2015)\nAlishah, H.N., Duarte, P., Peixe, T.: Conservative and dissipative polymatrix replicators. J. Dyn. Games 2(2), 157 (2015)\nAlishah, H.N., Duarte, P., Peixe, T.: Asymptotic Poincaré maps along the edges of polytopes. Nonlinearity 33(1), 469 (2019)\nAlishah, H.N., Duarte, P., Peixe, T.: Asymptotic dynamics of hamiltonian polymatrix replicators. Nonlinearity 36(6), 3182 (2023)\nAshwin, P., Postlethwaite, C.: On designing heteroclinic networks from graphs. Physica D 265, 26–39 (2013)\nBarendregt, N.W., Thomas, P.J.: Heteroclinic cycling and extinction in May–Leonard models with demographic stochasticity. J. Math. Biol. 86(2), 30 (2023)\nBunimovich, L.A., Webb, B.Z.: Isospectral compression and other useful isospectral transformations of dynamical networks. Chaos Interdiscip. J. Nonlinear Sci. 22, 3 (2012)\nCastro, S.B.S.D., Garrido-da Silva, L: Finite switching near heteroclinic networks. arXiv preprint arXiv:2211.04202 (2022)\nCastro, S.B.S.D., Labouriau, I.S., Podvigina, O.: A heteroclinic network in mode interaction with symmetry. Dyn. Syst. 25(3), 359–396 (2010)\nCastro, S.B., Ferreira, A., Garrido-da-Silva, L., Labouriau, I.S.: Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock. SIAM J. Appl. Dyn. Syst. 21(4), 2393–2431 (2022)\nField, M.J.: Lectures on Bifurcations, Dynamics and Symmetry. CRC Press (2020)\nField, M., Swift, J.W.: Stationary bifurcation to limit cycles and heteroclinic cycles. Nonlinearity 4(4), 1001 (1991)\nGarrido-da Silva, L., Castro, S.B.S.D.: Stability of quasi-simple heteroclinic cycles. Dyn. Syst. 34(1), 14–39 (2019)\nGaunersdorfer, A., Hofbauer, J.: Fictitious play, Shapley polygons, and the replicator equation. Games Econ. Behav. 11(2), 279–303 (1995)\nGuckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42. Springer (2013)\nHofbauer, J., Sigmund, K.: Permanence for replicator equations. In: Dynamical Systems, pp. 70–91. Springer (1987)\nHofbauer, J., Sigmund, K., et al.: Evolutionary Games and Population Dynamics. Cambridge University Press (1998)\nKatok, A., Hasselblatt, B.: Introduction to the Modern Theory of Dynamical Systems, vol. 54. Cambridge University Press (1997)\nKrupa, M., Melbourne, I.: Asymptotic stability of heteroclinic cycles in systems with symmetry. Ergodic Theory Dyn. Syst. 15(1), 121–147 (1995)\nLabouriau, I.S., Rodrigues, A.A.P.: On Takens’ last problem: tangencies and time averages near heteroclinic networks. Nonlinearity 30(5), 1876 (2017)\nLohse, A.: Unstable attractors: existence and stability indices. Dyn. Syst. 30(3), 324–332 (2015)\nMelbourne, I.: An example of a nonasymptotically stable attractor. Nonlinearity 4(3), 835 (1991)\nMilnor, J.: On the concept of attractor. In: The Theory of Chaotic Attractors, pp. 243–264. Springer (1985)\nPalis, J., de Melo, W.: Local stability. In: Geometric Theory of Dynamical Systems, pp. 39–90. Springer (1982)\nPeixe, T.: Lotka–Volterra Systems and Polymatrix Replicators. ProQuest LLC, Ann Arbor. Thesis (Ph.D.)–Universidade de Lisboa (Portugal) (2015)\nPeixe, T.: Permanence in polymatrix replicators. J. Dyn. Games (2019)\nPeixe, T., Rodrigues, A.: Persistent strange attractors in 3d polymatrix replicators. Physica D 438, 133346 (2022)\nPodvigina, O.: Stability and bifurcations of heteroclinic cycles of type z. Nonlinearity 25(6), 1887 (2012)\nPodvigina, O., Ashwin, P.: On local attraction properties and a stability index for heteroclinic connections. Nonlinearity 24(3), 887 (2011)\nPodvigina, O., Chossat, P.: Simple heteroclinic cycles. Nonlinearity 28(4), 901 (2015)\nPodvigina, O., Chossat, P.: Asymptotic stability of pseudo-simple heteroclinic cycles in \\(\\mathbb{R} ^{4}\\). J. Nonlinear Sci. 27(1), 343–375 (2017)\nPodvigina, O., Castro, S.B.S.D., Labouriau, I.S.: Stability of a heteroclinic network and its cycles: a case study from Boussinesq convection. Dyn. Syst. 34(1), 157–193 (2019)\nPodvigina, O., Castro, S.B.S.D., Labouriau, I.S.: Asymptotic stability of robust heteroclinic networks. Nonlinearity 33(4), 1757 (2020)\nPostlethwaite, C.M., Rucklidge, A.M.: Stability of cycling behaviour near a heteroclinic network model of Rock-Paper-Scissors-Lizard-Spock. Nonlinearity 35, 1702 (2021)\nRodrigues, A.A.P.: Persistent switching near a heteroclinic model for the geodynamo problem. Chaos Solitons Fractals 47, 73–86 (2013)\nRodrigues, A.A.P.: Attractors in complex networks. Chaos Interdiscip. J. Nonlinear Sci. 27(10), 103105 (2017)\nRuelle, D.: Elements of Differentiable Dynamics and Bifurcation Theory. Elsevier (2014)\nSmith, J.M., Price, G.R.: The logic of animal conflict. Nature 246(5427), 15–18 (1973)",{"EN":259},"This paper analyses the stability of cycles within a heteroclinic network formed by six cycles lying in a three-dimensional manifold, for a one-parameter model developed in the context of polymatrix replicator equations. We show the asymptotic stability of the network for a range of parameter values compatible with the existence of an interior equilibrium and we describe an asymptotic technique to decide which cycle (within the network) is visible in numerics. The technique consists of reducing the relevant dynamics to a suitable one-dimensional map, the so-called projective map. The stability of the fixed points of the projective map determines the stability of the associated cycles. The description of this new asymptotic approach is applicable to more general types of networks and is potentially useful in computational dynamics.",{"EN":261},"Stability of Heteroclinic Cycles: A New Approach Based on a Replicator Equation",{"VOID":263},"10.1007\u002Fs00332-023-09953-7","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00332-023-09953-7",[266,281],{"id":267,"sortIndex":167,"researcher":22,"roles":268,"affiliations":269,"properties":278},"7aafac60-bc68-4734-be04-531928184980",[169],[270],{"id":22,"sortIndex":23,"affiliation":271,"properties":22},{"id":272,"createTime":273,"updateTime":273,"relativeEntities":274,"slug":22,"properties":275,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"e6395d1f-4665-4382-80c6-34f600d87b2f","2024-02-18T15:44:40.584+00:00",[],{"title":276},{"VI":277},"Centro de Matemática and Faculdade de Ciências, Universidade do Porto, ISEG-Lisbon School of Economics and Management, Universidade de Lisboa, Lisbon, Portugal",{"title":279},{"VI":280},"Alexandre A. 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International Society for Optics and Photonics, pp. 93,940L–93,940L (2015)\nMalo, J., Laparra, V.: Psychophysically tuned divisive normalization approximately factorizes the PDF of natural images. Neural Comput. 22(12), 3179–3206 (2010)\nMalo, J., Ferri, F., Albert, J., Soret, J., Artigas, J.: The role of perceptual contrast non-linearities in image transform quantization. Image Vis. Comput. 18(3), 233–246 (2000)\nMalo, J., Epifanio, I., Navarro, R., Simoncelli, E.P.: Nonlinear image representation for efficient perceptual coding. IEEE Trans. Image Process. 15(1), 68–80 (2006)\nMartinez-Garcia, M., Cyria, P., Batard, T., Bertalmio, M., Malo, J.: Derivatives and inverse of cascaded linear+nonlinear neural models. PLoS ONE 13(10), e0201326 (2018). https:\u002F\u002Fdoi.org\u002F10.1371\u002Fjournal.pone.0201326\nMartinez-Garcia, M., Bertalmío, M., Malo, J.: In praise of artifice reloaded: caution with natural image databases in modeling vision. Front. 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Neurosci. 34(10), 3586–3596 (2014)\nSato, T., Haider, B., Hausser, M., Carandini, M.: An excitatory basis for divisive normalization in visual cortex. Nat. Neurosci. (2016). https:\u002F\u002Fdoi.org\u002F10.1038\u002Fnn.4249\nSchwartz, G., Rieke, F.: Nonlinear spatial encoding by retinal ganglion cells: when 1 + 1 \\(\\ne \\) 2. J. Gen. Physiol. 138(3), 283–290 (2011). https:\u002F\u002Fdoi.org\u002F10.1085\u002Fjgp.201110629\nSchwartz, O., Simoncelli, E.: Natural signal statistics and sensory gain control. Nat. Neurosci. 4(8), 819–825 (2001)\nSchwartz, O., Sejnowski, T.J., Dayan, P.: Perceptual organization in the tilt illusion. J. Vis. 9(4), 19 (2009). https:\u002F\u002Fdoi.org\u002F10.1167\u002F9.4.19\nSimoncelli, E.P., Heeger, D.J.: A model of neuronal responses in visual area MT. Vis. Res. 38(5), 743–761 (1998)\nSimoncelli, E.P., Freeman, W.T., Adelson, E.H., Heeger, D.J.: Shiftable multi-scale transforms. IEEE Trans. Inf. 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J. 12, 1–24 (1972)\nWilson, H.R., Cowan, J.D.: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13(2), 55–80 (1973)\nWilson, H.R., Humanski, R.: Spatial frequency adaptation and contrast gain control. Vis. Res. 33(8), 1133–1149 (1993)\nZeraati, R., et al.: Intrinsic timescales in the visual cortex change with selective attention and reflect spatial connectivity. Nat. Commun. 14(1), 1858 (2023)",{"EN":340},"Divisive Normalization and the Wilson–Cowan equations are well-known influential models of nonlinear neural interaction (Carandini and Heeger in Nat Rev Neurosci 13(1):51, 2012; Wilson and Cowan in Kybernetik 13(2):55, 1973). However, they have been always treated as different approaches and have not been analytically related yet. In this work, we show that Divisive Normalization can be derived from the Wilson–Cowan dynamics. Specifically, assuming that Divisive Normalization is the steady state of the Wilson–Cowan differential equations, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson–Cowan kernel but also depends on the signal. A standard stability analysis of a Wilson–Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability suggests the appropriateness of our steady state assumption. The proposed theory provides a mechanistic foundation for the suggestions that have been done on the need of signal-dependent Divisive Normalization in Coen-Cagli et al. (PLoS Comput Biol 8(3):e1002405, 2012). Moreover, this theory explains the modifications that had to be introduced ad hoc in Gaussian kernels of Divisive Normalization in Martinez-Garcia et al. (Front Neurosci 13:8, 2019) to reproduce contrast responses in V1 cortex. Finally, the derived relation implies that the Wilson–Cowan dynamics also reproduce visual masking and subjective image distortion, which up to now had been explained mainly via Divisive Normalization.",{"EN":342},"Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics",{"VOID":344},"10.1007\u002Fs00332-023-10009-z","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00332-023-10009-z",[347,362,374],{"id":348,"sortIndex":167,"researcher":22,"roles":349,"affiliations":350,"properties":359},"d5b897c5-034f-4243-a928-9d650644bc14",[169],[351],{"id":22,"sortIndex":23,"affiliation":352,"properties":22},{"id":353,"createTime":354,"updateTime":354,"relativeEntities":355,"slug":22,"properties":356,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"3feb64e2-c4ea-4590-b54d-d0f00a2094ec","2024-01-25T06:16:16.144+00:00",[],{"title":357},{"VI":358},"Image Processing Lab, Universitat de València, Valencia, Spain",{"title":360},{"VI":361},"José Juan Esteve-Taboada",{"id":363,"sortIndex":23,"researcher":22,"roles":364,"affiliations":365,"properties":371},"fecb6648-cce6-4109-8ca0-395bce79979c",[169],[366],{"id":22,"sortIndex":23,"affiliation":367,"properties":22},{"id":353,"createTime":354,"updateTime":354,"relativeEntities":368,"slug":22,"properties":369,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},[],{"title":370},{"VI":358},{"title":372},{"VI":373},"Jesús Malo",{"id":375,"sortIndex":376,"researcher":22,"roles":377,"affiliations":378,"properties":388},"b1325376-ae85-4ea2-a8a7-45532c61cff9",2,[169],[379],{"id":22,"sortIndex":23,"affiliation":380,"properties":22},{"id":381,"createTime":382,"updateTime":382,"relativeEntities":383,"slug":384,"properties":385,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"3e0491d5-9544-472c-b211-35a21c172e0b","2024-04-16T16:42:03.929+00:00",[],"Spanish-National-Research-Council-CSIC-Madrid-Spain",{"title":386},{"EN":387},"Spanish National Research Council CSIC, Madrid, Spain",{"title":389},{"VI":390},"Marcelo Bertalmío",{"url":345,"publisher":392,"properties":421},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":393,"slug":10,"properties":394,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":399,"manageAffiliations":400,"indexDatabases":401,"url":22,"thumbnailPath":22,"statistic":416,"gsStatistic":22,"type":140,"analyzePriority":22},[],{"issn":395,"eissn":396,"title":397,"url":398},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},[],[],[402,409],{"id":95,"indexDatabase":403,"url":108,"indexYears":109,"academicFieldIds":408,"indexDatabaseRanking":114},{"id":97,"createTime":98,"updateTime":99,"relativeEntities":404,"label":405,"description":406,"key":105,"publicationTags":407,"standard":22},[],{"EN":102,"VI":102},{"EN":102,"VI":104},[107],[111,112,113],{"id":74,"indexDatabase":410,"url":89,"indexYears":22,"academicFieldIds":415,"indexDatabaseRanking":22},{"id":76,"createTime":77,"updateTime":78,"relativeEntities":411,"label":412,"description":413,"key":85,"publicationTags":414,"standard":22},[],{"EN":81,"VI":81},{"VI":83,"EN":84},[87,88],[91,92,93],{"impactFactor":23,"impactFactorByYear":417,"i10Index":23,"i10IndexLast5Year":23,"totalPublication":117,"totalPublicationByYear":418,"totalCitation":23,"totalCitationByYear":419,"totalCitationPerPublication":23,"totalCitationPerPublicationByYear":420,"hindexLast5Year":23,"hindex":23},{},{"1991":69,"1992":119,"1993":120,"1994":121,"1995":122,"1996":123,"1997":124,"1998":122,"1999":122,"2000":125,"2001":126,"2002":69,"2003":120,"2004":122,"2005":125,"2006":69,"2007":127,"2008":123,"2009":120,"2010":121,"2011":122,"2012":128,"2013":127,"2014":129,"2015":130,"2016":131,"2017":132,"2018":131,"2019":133,"2020":134,"2021":135,"2022":136,"2023":137,"2024":123},{},{},{"volume":422,"pages":424},{"VOID":423},"34",{"VOID":425},"1-36","2024-02-15",2024,{"id":429,"createTime":430,"updateTime":431,"relativeEntities":432,"slug":433,"properties":434,"entityType":160,"verifyStatus":161,"verifyTime":431,"verifyNote":162,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":443,"fullTextUrl":22,"authors":444,"publicationType":210,"publisherRelationship":475,"citationCount":22,"citationInfo":22,"publishDate":510,"publishYear":511,"citationAnalyzeStatus":21,"lastCitationAnalyze":22,"indexDatabases":22,"openAccess":22,"references":22,"isForceReanalyzing":248},"9e0e771e-9a84-4c6f-ad63-154d29d1215e","2024-02-09T07:42:51.699+00:00","2025-02-13T23:51:27.279+00:00",[],"Gyroscopic-control-and-stabilization",{"references":435,"abstract":437,"title":439,"doi":441},{"VOID":436},"Abraham, R. & J. 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Marsden, “Controlling Homoclinic Orbits,”Theoretical and Computational Fluid Mechanics (1989), pp. 179–190.\nBloch, A. M. & J. E. Marsden, “Stabilization of Rigid Body Dynamics by the Energy-Casimir Method,”Systems and Control Letters,14, (1990), pp. 341–346.\nBrockett, R. W., “Feedback Invariants for Nonlinear Systems,”6th IFAC Congress, Helsinki (1978), pp. 1115–1120.\nChetayev, N. G.,The Stability of Motion, Pergamon Press, 1961.\nCrouch, P. E. & Van Der Schaft,Variational and Hamiltonian Control Systems, Springer-Verlag, 1987.\nGodbillon, C.,Géometrie différentielle et mécanique analytique, Hermann, Paris, 1969.\nGotay, M. J. & J. M. Nester, “Presymplectic Lagrangian Systems I: the constraint algorithm and the equivalence theorem,”Ann. Inst. Henri Poincaré-Section A,30(2) (1979), pp. 129–142.\nGotay, M. J. & J. M. Nester, “Presymplectic Lagrangian Systems II: the second-order equation problem,”Ann. Inst. Henri Poincaré-Section A,32(1) (1980), pp. 1–13.\nGrossman, R., P. S. Krishnaprasad, & J. E. Marsden, “The Dynamics of Two Coupled Three Dimensional Rigid Bodies,” inDynamical Systems Approaches to Nonlinear Problems in Systems and Circuits, F. Salam & M. Levi, eds., SIAM, Philadelphia, 1988, pp. 373–378.\nGuillemin, V. & S. Sternberg,Symplectic Techniques in Physics, Cambridge University Press, Cambridge, 1984.\nHan, J. H.,Symmetries in Nonlinear Control Systems and Their Applications, Ph.D. Dissertation, Electrical Engineering Department, University of Maryland, College Park, 1986.\nHermann, R.,Differential Geometry and the Calculus of Variation, 2nd ed., Math. Sci. Press, 1977.\nHolm, D., J. E. Marsden, T. Ratiu, & A. Weinstein, “Nonlinear Stability of Fluid and Plasma Equilibria,”Physics Report,123(1985), pp. 1–116.\nIsidori, A.,Nonlinear Control Systems, 2nd ed., Springer-Verlag, 1989.\nJakubczyk, B., “Hamiltonian Realizations of Nonlinear Systems,” inTheory and Applications of Nonlinear Control Systems, C. I. Byrnes & A. Lindquist, eds., North-Holland, 1986, pp. 261–271.\nKrishnaprasad, P. S., “Lie-Poisson Structures, Dual-spin Spacecraft and Asymptotic Stability,”Nonlinear Analysis: Theory, Methods, and Applications,7(1984), pp. 1011–1035.\nKrishnaprasad, P. S., “Eulerian Many-Body Problems,” Systems Research Center, University of Maryland, College Park, SRC TR-89-15, 1989, also inContemp. Math., Vol. 97, pp. 187–208, AMS.\nKrishnaprasad, P. S. & C. A. Berenstein, “On the Equilibria of Rigid Spacecraft with Rotors,”Systems & Control Letters,4(1984), pp. 157–163.\nLanczos, C.,The Variational Principles of Mechanics, 4th ed., University of Toronto Press, 1970.\nLewis, D., “Lagrangian Block Diagonalization,”J. Dynamics and Differential Equations (1991), (to appear).\nLibermann, P. & C-M. Marie,Symplectic Geometry and Analytical Mechanics, Dordrecht: D. Reidel Publ., 1987.\nMaddocks, J. H., “Stability and Folds,”Archive for Rational Mechanics and Analysis,99(4) (1987), pp. 301–328.\nMarmo, G., E. J. Saletan, & A. Simoni, “Reduction of Symplectic Manifolds Through Constants of the Motion,”Nuovo Cimento,50B(1) (1979).\nMarsden, J. E. & T. Ratiu, “Reduction of Poisson Manifolds,”Letters in Math. Phys.,11 (1986), pp. 161–169.\nMarsden, J. E. & A. Weinstein, “Reduction of Symplectic Manifolds with Symmetry,”Reports in Math. Phys.,5(1974), pp. 121–130.\nNijmeijer, H. & Van Der Schaft,Nonlinear Dynamical Control Systems, Springer-Verlag, 1990.\nNomizu, K.,Lie Groups and Differential Geometry, The Mathematical Society of Japan, 1956.\nPalais, R. S., “The Principle of Symmetric Criticality,”Comm. in Math. Physics,69(1) (1979), pp. 19–30.\nPosbergh, T, J. C. Simo & J. E. Marsden, “Stability Analysis of a Rigid Body with Attached Geometrically Nonlinear Appendage by the Energy-Momentum Method,” inDynamics and Control of Multibody Systems, J. E. Marsden, P. S. Krishnaprasad, & J. C. Simo, eds., AMS, 1988, pp. 371–397,Contemporary Mathematics, Vol. 97.\nRouth, E.,The Advanced Part of a Treatise on the Dynamics of a System of Rigid Bodies, 4th ed., Dover Publications, Inc., 1884.\nSiam,Report on the Panel on Future Directions in Control Theory: a Mathematical Perspective, Philadelphia, 1988.\nSimo, J. C., D. Lewis, & J. E. Marsden, “Stability of Relative Equilibria, Part I: The Reduced Energy-Momentum Method,” Division of Applied Mechanics, Stanford University, SUDAM Report No. 89-3, 1989, (to appear inArchive for Rational Mechanics and Analysis, 1990).\nSimo, J. C., T. Posbergh & J. E. Marsden, “Nonlinear Stability of Geometrically Exact Rods by the Energy-Momentum Method,” Stanford University, Division of Applied Mechanics, preprint, 1989.\nSimo, J. C., T. Posbergh & J. E. Marsden, “Stability of Relative Equilibria, Part II: Application to Nonlinear Elasticity,” Stanford University, Division of Applied Mechanics, preprint, 1989, (to appear inArchive for Rational Mechanics and Analysis, 1990).\nSmale, S., “Topology and Mechanics I, II,”Inventiones Mathematicae,10,11 (1970), pp. 305–331, 45–64.\nSouriau, J. M.,Structure des systémes dynamique, Dunod, Paris, 1970.\nSternberg, S.,Lectures on Celestial Mechanics: Iand II, Addison-Wesley, 1969.\nVershik, A. M. & L. D. Faddeev, “Lagrangian Mechanics in Invariant Form,”Sel. Math. Sov.,1, 4 (1981), pp. 339–350.\nWang, L.-S.,Geometry, Dynamics and Control of Coupled Systems, Ph.D. Dissertation, Electrical Engineering Department, University of Maryland, College Park, August, 1990.\nWang, L.-S. & P. S. Krishnaprasad, “Relative Equilibria of Two Rigid Bodies connected by a Ball-in-Socket Joint,”Proc. of the 1989 IEEE Conference on Decision and Control, Tampa, FL (Dec. 1989), pp. 692–697.\nWang, L.-S. & P. S. Krishnaprasad, “A Multibody Analog of the Dual-Spin Problems,”Proc. of the 29th IEEE Conference on Decision and Control, Honolulu, Hawaii (Dec. 1990), pp. 1294–1299.\nWang, L.-S., P. S. Krishnaprasad & J. H. Maddocks, “Hamiltonian Dynamics of a Rigid Body in a Central Gravitational Field,”Celestial Mechanics and Dynamical Astronomy,50(4) (1991), pp. 349–386.\nWeinstein, A., “Stability of Poisson-Hamilton Equilibria,” inFluids and Plasmas: Geometry and Dynamics, J. E. Marsden, ed., 1984, in seriesContemporary Mathematics,28, pp. 3–13, AMS, Providence.\nWhittaker, E. T.,A Treatise on the Analytical Dynamics of Panicles and Rigid Bodies, 4th ed., Cambridge University Press, Cambridge, 1959.\nWillmore, T. J., “The Definition of Lie Derivative,”Proc. Edin. Math. Soc.,12(2) (1960), pp. 27–29.\nWong, S. K., “Field and Particle Equations for the Classical Yang-Mills Field and Particles with Isotopic Spin,”Nuovo Cimento,65A (1970), pp. 689–693.\nYang, R. & P. S. Krishnaprasad, “On the Dynamics of Four-Bar Linkages, Part II: Bifurcations of Relative Equilibria,”Proc. of the 1990 IEEE Conference on Decision and Control, Honolulu, Hawaii (Dec. 1990).",{"EN":438},"In this paper, we consider the geometry of gyroscopic systems with symmetry, starting from an intrinsic Lagrangian viewpoint. We note that natural mechanical systems with exogenous forces can be transformed into gyroscopic systems, when the forces are determined by a suitable class of feedback laws. To assess the stability of relative equilibria in the resultant feedback systems, we extend the energy-momentum block-diagonalization theorem of Simo, Lewis, Posbergh, and Marsden to gyroscopic systems with symmetry. We illustrate the main ideas by a key example of two coupled rigid bodies with internal rotors. The energy-momentum method yields computationally tractable stability criteria in this and other examples.",{"EN":440},"Gyroscopic control and stabilization",{"VOID":442},"10.1007\u002FBF01209527","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF01209527",[445,460],{"id":446,"sortIndex":23,"researcher":22,"roles":447,"affiliations":448,"properties":457},"41e2733a-bf63-4dcf-8335-208ca7f970ce",[169],[449],{"id":22,"sortIndex":23,"affiliation":450,"properties":22},{"id":451,"createTime":452,"updateTime":452,"relativeEntities":453,"slug":22,"properties":454,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"4dc243f5-0562-42a9-b100-2190fd4f4447","2023-12-19T11:38:48.521+00:00",[],{"title":455},{"VI":456},"Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan, R.O.C.",{"title":458},{"VI":459},"L. -S. Wang",{"id":461,"sortIndex":167,"researcher":22,"roles":462,"affiliations":463,"properties":472},"4238d57a-7fba-4715-b4e1-570c908c008e",[169],[464],{"id":22,"sortIndex":23,"affiliation":465,"properties":22},{"id":466,"createTime":467,"updateTime":467,"relativeEntities":468,"slug":22,"properties":469,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"4238f641-7b4d-40f4-877c-b5ee823fab93","2024-02-09T07:42:51.943+00:00",[],{"title":470},{"VI":471},"Electrical Engineering Department & Systems Research Center, University of Maryland, College Park, USA",{"title":473},{"VI":474},"P. S. 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Sontag",{"url":22,"publisher":546,"properties":22},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":547,"slug":10,"properties":548,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":553,"manageAffiliations":554,"indexDatabases":555,"url":22,"thumbnailPath":22,"statistic":570,"gsStatistic":22,"type":140,"analyzePriority":22},[],{"issn":549,"eissn":550,"title":551,"url":552},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},[],[],[556,563],{"id":95,"indexDatabase":557,"url":108,"indexYears":109,"academicFieldIds":562,"indexDatabaseRanking":114},{"id":97,"createTime":98,"updateTime":99,"relativeEntities":558,"label":559,"description":560,"key":105,"publicationTags":561,"standard":22},[],{"EN":102,"VI":102},{"EN":102,"VI":104},[107],[111,112,113],{"id":74,"indexDatabase":564,"url":89,"indexYears":22,"academicFieldIds":569,"indexDatabaseRanking":22},{"id":76,"createTime":77,"updateTime":78,"relativeEntities":565,"label":566,"description":567,"key":85,"publicationTags":568,"standard":22},[],{"EN":81,"VI":81},{"VI":83,"EN":84},[87,88],[91,92,93],{"impactFactor":23,"impactFactorByYear":571,"i10Index":23,"i10IndexLast5Year":23,"totalPublication":117,"totalPublicationByYear":572,"totalCitation":23,"totalCitationByYear":573,"totalCitationPerPublication":23,"totalCitationPerPublicationByYear":574,"hindexLast5Year":23,"hindex":23},{},{"1991":69,"1992":119,"1993":120,"1994":121,"1995":122,"1996":123,"1997":124,"1998":122,"1999":122,"2000":125,"2001":126,"2002":69,"2003":120,"2004":122,"2005":125,"2006":69,"2007":127,"2008":123,"2009":120,"2010":121,"2011":122,"2012":128,"2013":127,"2014":129,"2015":130,"2016":131,"2017":132,"2018":131,"2019":133,"2020":134,"2021":135,"2022":136,"2023":137,"2024":123},{},{},{"total":135,"publishYear":22,"statisticByYear":576},{"2012":376,"2013":376,"2014":577,"2015":119,"2016":119,"2018":167,"2019":119,"2020":578,"2021":167,"2022":167,"2023":376},3,5,"2003-01-01",2003,"ERROR_IN_ANALYZE_CITATION","2024-04-13T18:46:11.749+00:00",[],{"id":585,"createTime":586,"updateTime":587,"relativeEntities":588,"slug":589,"properties":590,"entityType":160,"verifyStatus":161,"verifyTime":587,"verifyNote":162,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":599,"fullTextUrl":22,"authors":600,"publicationType":210,"publisherRelationship":631,"citationCount":22,"citationInfo":22,"publishDate":666,"publishYear":667,"citationAnalyzeStatus":21,"lastCitationAnalyze":22,"indexDatabases":22,"openAccess":22,"references":22,"isForceReanalyzing":248},"0a11bd93-6e13-42ae-950a-cd13de725a9f","2024-02-12T05:44:51.556+00:00","2025-01-03T23:50:55.699+00:00",[],"Poincar%C3%A9-s-Equations-for-Cosserat-Media-Application-to-Shells",{"references":591,"abstract":593,"title":595,"doi":597},{"VOID":592},"Antman, S.S.: Nonlinear problems of elasticity. In: Mathematical Sciences, vol. 107. Springer, New York (2005)\nArnold, V.I.: Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l’hydrodynamique des fluides parfaits. Ann. Inst. J. Fourier 16(1), 319–361 (1966)\nArnold, V.I.: Mathematical Methods in Classical Mechanics, 2nd edn. Springer, New-York (1988)\nBoyer, F., Primault, D.: The Poincaré–Chetayev equations and flexible multibody systems. J. Appl. Math. Mech. 69(6), 925–942 (2005). http:\u002F\u002Fhal.archives-ouvertes.fr\u002Fhal--00672477\nBoyer, F., Porez, M., Khalil, W.: Macro-continuous computed torque algorithm for a three-dimensional eel-like robot. IEEE Trans. Robot. 22(4), 763–775 (2006)\nBoyer, F., Porez, M., Leroyer, A., Visonneau, M.: Fast dynamics of an eel-like robot-comparisons with Navier–Stokes simulations. IEEE Trans. Robot. 24(6), 1274–1288 (2008)\nBoyer, F., Porez, M., Leroyer, A.: Poincaré–Cosserat equations for the Lighthill three-dimensional large amplitude elongated body theory: Application to robotics. J. Nonlinear Sci. 20, 47–79 (2010)\nBoyer, F., Ali, S., Porez, M.: Macro-continuous dynamics for hyper-redundant robots: application to kinematic locomotion bio-inspired by elongated body animals. IEEE Trans. Robot. 28(2), 303–317 (2012)\nCastrillón López, M., Ratiu, T.S., Shkoller, S.: Reduction in principal fiber bundles: covariant Euler–Poincaré equations. Proc. Am. Math. Soc. 128(7), 2155–2164 (2000)\nCosserat, E., Cosserat, F.: Théorie des corps déformables. Hermann, Paris (1909)\nDemoures, F., Gay-Balmaz, F., Kobilarov, M., Ratiu, T.S.: Multisymplectic lie group variational integrator for a geometrically exact beam in r3. Commun. Nonlinear Sci. Numer. Simul. 19(10), 3492–3512 (2014)\nEbin, D.G., Marsden, J.E.: Groups of diffeomorphism and the motion of an incompressible fluid. Ann. Math 92, 102–163 (1970)\nEllis, D.C.P., Gay-Balmaz, F., Holm, D.D., Putkaradze, V., Ratiu, T.S.: Symmetry reduced dynamics of charged molecular strands. Arch. Ration. Mech. Anal. 197(3), 811–902 (2010)\nEringen, A.C.: Microcontinuum Field Theories I: Foundations and Solids. Springer, New York (1998)\nFox, D.D., Simo, J.C.: A drill rotation formulation for geometrically exact shells. Comput. Methods Appl. Mech. Eng. 98, 329–343 (1992)\nGay-Balmaz, F., Holm, D.D., Ratiu, T.S.: Variational principles for spin systems and the Kirchhoff rod. J. Geom. Mech. 1(4), 417–444 (2009)\nGreen, A.E., Naghdi, P.M.: Non-isothermal theory of rods, plates and shells. Int. J. Solids Struct. 6, 209–244 (1970)\nGreen, A.E., Naghdi, P.M.: On the derivation of shell theories by direct approach. J. Appl. Mech. 41(1), 173–176 (1974)\nGreen, A.E., Zerna, W.: Theoretical Elasticity. Clarendon Press, Oxford (1960). end ed. edition\nHolm, D.D., Marsden, J.E., Ratiu, T.S.: The Euler–Poincaré equations and semidirect products with applications to continuum theories. Adv. Math. 137, 1–81 (1998)\nHolm, D.D., Putkaradze, V.: Nonlocal orientation-dependent dynamics of charged strands and ribbons. C. R. Acad. Sci. Paris Ser. I 347, 1093–1098 (2009)\nLibai, A., Simmonds, J.G.: The Nonlinear Theory of Elastic Shells, 2nd edn. Cambridge University Press, Cambridge (1998)\nLichnerowicz, A.: Elements de Calcul Tensoriel. Jacques Gabay, Paris (1987)\nMalvern, L.E.: Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, New-Jersey (1969)\nMarle, C.-M.: On Henri Poincaré’s note: “sur une forme nouvelle des equations de la mécanique”. J. Geom. Symmetry Phys. 29, 1–38 (2013)\nMarsden, J.E., Montgomery, R., Ratiu, T.S.: Reduction, symmetry, and phases in mechanics. In: Memoirs of the American Mathematical Society, vol. 88 (436). American Mathematical Society (1990)\nMarsden, J.E., Hughes, T.J.R.: Mathematical Foundations of Elasticity, 1st edn. Dover, Mineola (1994)\nMarsden, J.E., Ratiu, T.S.: Introduction to Mechanics and Symmetry, 2nd edn. Springer, New York (1999)\nMilne-Thomson, L.M.: Theoretical Hydrodynamics. Macmillan, London (1938)\nPoincaré, H.: Sur une forme nouvelle des équations de la mécanique. Compte Rendu de l’Académie des Sciences de Paris 132, 369–371 (1901)\nPommaret, J.F.: Partial Differential Equations and Group Theory, 1st edn. Springer, Netherlands (1994)\nReissner, E.: The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12, 69–76 (1945)\nRenda, F., Giorelli, M., Calisti, M., Cianchetti, M., Laschi, C.: Dynamic model of a multibending soft robot arm driven by cables. IEEE Trans. Robot. 30(5), 1109–1122 (2014)\nSimmonds, J.G., Danielson, D.A.: Nonlinear shell theory with finite rotation and stress-function vectors. J. Appl. Mech. 39, 1085–1090 (1972)\nSimo, J.C., Fox, D.D.: On a stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization. Comput. Methods Appl. Mech. Eng. 72(3), 267–304 (1989)\nSimo, J.C., Marsden, J.E., Krishnaprasad, P.S.: The hamiltonian structure of nonlinear elasticity: the material and convective representations of solids, rods, and plates. Arch. Ration. Mech. Anal. 104, 125–183 (1988)\nSimo, J.C., Rifai, M.S., Fox, D.D.: On a stress resultant geometrically exact shell model. part vi: conserving algorithms for non-linear dynamics. Int. J. Numer. Methods Eng. 34, 117–164 (1992)\nSimo, J.C., Vu-Quoc, L.: On the dynamics in space of rods undergoing large motions—a geometrically exact approach. Comput. Methods Appl. Mech. Eng. 66(2), 125–161 (1988)\nSpencer, D.C.: Overdetermined systems of partial differential equations. Bull. Am. Math. Soc. 75, 1–114 (1965)\nThomas, J.R., Hughes, Brezzi, F.: On drilling degrees of freedom. Comput. Methods Appl. Mech. Eng. 72, 105–121 (1989)\nToupin, R.A.: Theories of elasticity with couple-stress. Arch. Rational Mech. Anal. 17, 85–112 (1964)\nVerl, A., Albu-Schaeffer, A., Brock, O. (eds). Soft Robotics: Transferring Theory to Application. Springer, New York (2015)\nVu-Quoc, L.: On the algebra of two point tensors and their applications. Z. Angew. Math. Mech.: ZAMM 76(9), 540–541 (1996)\nWeymouth, G.D., Triantafyllou, M.S.: Ultra-fast escape of a deformable jet-propelled body. J. Fluid Mech. 721, 367–385 (2013)",{"EN":594},"In 1901, Henri Poincaré discovered a new set of equations for mechanics. These equations are a generalization of Lagrange’s equations for a system whose configuration space is a Lie group which is not necessarily commutative. Since then, this result has been extensively refined through the Lagrangian reduction theory. In the present contribution, we apply an extended version of these equations to continuous Cosserat media, i.e. media in which the usual point particles are replaced by small rigid bodies, called microstructures. In particular, we will see how the shell balance equations used in nonlinear structural dynamics can be easily deduced from this extension of the Poincaré’s result. In future, these results will be used as foundations for the study of squid locomotion, which is an emerging topic relevant to soft robotics.",{"EN":596},"Poincaré’s Equations for Cosserat Media: Application to Shells",{"VOID":598},"10.1007\u002Fs00332-016-9324-7","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00332-016-9324-7",[601,616],{"id":602,"sortIndex":167,"researcher":22,"roles":603,"affiliations":604,"properties":613},"c0b1a1ae-63fc-4ab3-847c-6fd159f73874",[169],[605],{"id":22,"sortIndex":23,"affiliation":606,"properties":22},{"id":607,"createTime":608,"updateTime":608,"relativeEntities":609,"slug":22,"properties":610,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"ce06d3cf-0de8-4c63-b99e-fde5127d45a4","2024-02-12T05:44:51.604+00:00",[],{"title":611},{"VI":612},"Khalifa University, KURI, Abu Dhabi, UAE",{"title":614},{"VI":615},"Federico Renda",{"id":617,"sortIndex":23,"researcher":22,"roles":618,"affiliations":619,"properties":628},"d686f65f-4ceb-440a-8b8f-b9efc2810fed",[169],[620],{"id":22,"sortIndex":23,"affiliation":621,"properties":22},{"id":622,"createTime":623,"updateTime":623,"relativeEntities":624,"slug":22,"properties":625,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"a227d094-b0f8-4e7e-ba2f-4e420f51fe77","2024-01-29T23:03:14.747+00:00",[],{"title":626},{"VI":627},"EMN, IRCCyN, Nantes Cedex 3, France",{"title":629},{"VI":630},"Frederic Boyer",{"url":599,"publisher":632,"properties":661},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":633,"slug":10,"properties":634,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":639,"manageAffiliations":640,"indexDatabases":641,"url":22,"thumbnailPath":22,"statistic":656,"gsStatistic":22,"type":140,"analyzePriority":22},[],{"issn":635,"eissn":636,"title":637,"url":638},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},[],[],[642,649],{"id":95,"indexDatabase":643,"url":108,"indexYears":109,"academicFieldIds":648,"indexDatabaseRanking":114},{"id":97,"createTime":98,"updateTime":99,"relativeEntities":644,"label":645,"description":646,"key":105,"publicationTags":647,"standard":22},[],{"EN":102,"VI":102},{"EN":102,"VI":104},[107],[111,112,113],{"id":74,"indexDatabase":650,"url":89,"indexYears":22,"academicFieldIds":655,"indexDatabaseRanking":22},{"id":76,"createTime":77,"updateTime":78,"relativeEntities":651,"label":652,"description":653,"key":85,"publicationTags":654,"standard":22},[],{"EN":81,"VI":81},{"VI":83,"EN":84},[87,88],[91,92,93],{"impactFactor":23,"impactFactorByYear":657,"i10Index":23,"i10IndexLast5Year":23,"totalPublication":117,"totalPublicationByYear":658,"totalCitation":23,"totalCitationByYear":659,"totalCitationPerPublication":23,"totalCitationPerPublicationByYear":660,"hindexLast5Year":23,"hindex":23},{},{"1991":69,"1992":119,"1993":120,"1994":121,"1995":122,"1996":123,"1997":124,"1998":122,"1999":122,"2000":125,"2001":126,"2002":69,"2003":120,"2004":122,"2005":125,"2006":69,"2007":127,"2008":123,"2009":120,"2010":121,"2011":122,"2012":128,"2013":127,"2014":129,"2015":130,"2016":131,"2017":132,"2018":131,"2019":133,"2020":134,"2021":135,"2022":136,"2023":137,"2024":123},{},{},{"volume":662,"pages":664},{"VOID":663},"27",{"VOID":665},"1-44","2016-07-28",2016,{"id":669,"createTime":670,"updateTime":671,"relativeEntities":672,"slug":673,"properties":674,"entityType":160,"verifyStatus":161,"verifyTime":671,"verifyNote":162,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":683,"fullTextUrl":22,"authors":684,"publicationType":210,"publisherRelationship":726,"citationCount":22,"citationInfo":22,"publishDate":761,"publishYear":762,"citationAnalyzeStatus":21,"lastCitationAnalyze":22,"indexDatabases":22,"openAccess":22,"references":22,"isForceReanalyzing":248},"fb326d6b-9cef-455d-90c0-2262ca2db30f","2024-02-09T19:12:10.276+00:00","2024-12-27T23:49:56.237+00:00",[],"Hopf-Like-Bifurcations-and-Asymptotic-Stability-in-a-Class-of-3D-Piecewise-Linear-Systems-with-Applications",{"references":675,"abstract":677,"title":679,"doi":681},{"VOID":676},"Cardoso, J.L., Llibre, J., Novaes, D.D., Tonon, D.J.: Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields. Dyn. Syst. 35(3), 124818 (2020)\nCastillo, J., Llibre, J., Verduzco, F.: The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems. Nonlinear Dyn. 90, 1829–1840 (2017)\nCristiano, R., Pagano, D.J.: Two-parameter boundary equilibrium bifurcations in 3D-Filippov systems. J. Nonlinear Sci. 29(6), 2845–2875 (2019)\nCristiano, R., Pagano, D.J., Freire, E., Ponce, E.: Revisiting the Teixeira singularity bifurcation analysis. Application to the control of power converters. Int. J. Bifurc. Chaos 28(9), 1850106 (2018)\nCristiano, R., Pagano, D.J., Carvalho, T., Tonon, D.J.: Bifurcations at a degenerate two-fold singularity and crossing limit cycles. J. Differ. Equ. 268(1), 115–140 (2019a)\nCristiano, R., Ponce, E., Pagano, D.J., Granzotto, M.: On the Teixeira singularity bifurcation in a dc-dc power electronic converter. Nonlinear Dyn. 96(2), 1243–1266 (2019b)\ndi Bernardo, M., Johansson, K.H., Vasca, F.: Self-oscillations and sliding in relay feedback systems: symmetry and bifurcations. Int. J. Bifurc. Chaos 11(04), 1121–1140 (2001)\nde Carvalho, T., Cristiano, R., Gonçalves, L.F., Tonon, D.J.: Global analysis of the dynamics of a mathematical model to intermittent HIV treatment. Nonlinear Dyn. 101, 719–739 (2020)\nde Freitas, B.R., Llibre, J., Medrado, J.C.: Limit cycles of continuous and discontinuous piecewise-linear differential systems in R3. J. Comput. Appl. Math. 338, 311–323 (2018)\nDumortier, F., Llibre, J., Artés, J.: Qualitative Theory Of Planar Differential Systems. Universitext. Springer, Berlin (2006)\nEuzébio, R.D., Llibre, J.: On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line. J. Math. Anal. Appl. 424(1), 475–486 (2015)\nFilippov, A.F.: Differential equations with discontinuous righthand sides, volume 18 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1988. Translated from the Russian\nFreire, E., Ponce, E., Torres, F.: Hopf-like bifurcations in planar piecewise linear systems. Publicacions Matemátiques 41, 135–148 (1997)\nFreire, E., Ponce, E., Torres, F.: Canonical discontinuous planar piecewise linear systems. SIAM J. Appl. Dyn. Syst. 11(1), 181–211 (2012)\nFreire, E., Ponce, E., Torres, F.: A general mechanism to generate three limit cycles in planar Filippov systems with two zones. Nonlinear Dyn. 78(1), 251–263 (2014)\nHarris, J., Ermentrout, B.: Bifurcations in the Wilson–Cowan equations with nonsmooth firing rate. SIAM J. Appl. Dyn. Syst. 14(1), 43–72 (2015)\nJacquemard, A., Tonon, D.J.: Coupled systems of non-smooth differential equations. Bull. Sci. Math. 136(3), 239–255 (2012)\nJacquemard, A., Teixeira, M.A., Tonon, D.J.: Piecewise smooth reversible dynamical systems at a two-fold singularity. Int. J. Bifurc. Chaos Appl. Sci. Eng. 22(8), 1250192 (2012)\nJacquemard, A., Teixeira, M.A., Tonon, D.J.: Stability conditions in piecewise smooth dynamical systems at a two-fold singularity. J. Dyn. Control Syst. 19(1), 47–67 (2013)\nKuznetsov, Y.A., Rinaldi, S., Gragnani, A.: One-parameter bifurcations in planar Filippov systems. Int. J. Bifurc. Chaos 13(8), 2157–2188 (2003)\nLlibre, J., Novaes, D.D., Teixeira, M.A.: Maximum number of limit cycles for certain piecewise linear dynamical systems. Nonlinear Dyn. 82, 1159–1175 (2015)\nOlivar, G., Angulo, F., di Bernardo, M.: Hopf-like transitions in nonsmooth dynamical systems. In: 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), vol. 4, pp. IV–693 (2004)\nRodrigues, D.S., Mancera, P.F.A., Carvalho, T., Gonçalves, L.F.: Sliding mode control in a mathematical model to chemoimmunotherapy: The occurrence of typical singularities. Applied Mathematics and Computation, Elsevier, vol. 387, p. 124782 (2020)\nSimpson, D.J.W.: A compendium of Hopf-like bifurcations in piecewise-smooth dynamical systems. Phys. Lett. A 382(35), 2439–2444 (2018)\nSimpson, D.: Hopf-like boundary equilibrium bifurcations involving two foci in Filippov systems. J. Differ. Equ. 267(11), 6133–6151 (2019)\nUtkin, V.: Discussion aspects of high-order sliding mode control. IEEE Trans. Autom. Control 61(3), 829–833 (2016)\nZou, F., Nossek, J.A.: Hopf-like bifurcation in cellular neural networks. In: 1993 IEEE International Symposium on Circuits and Systems, vol. 4, pp. 2391–2394 (1993)",{"EN":678},"The main purpose of this paper is to analyze the Hopf-like bifurcations in 3D piecewise linear systems. Such bifurcations are characterized by the birth of a piecewise smooth limit cycle that bifurcates from a singular point located at the discontinuity manifold. In particular, this paper concerns systems of the form \n                \n                  \n                \n                $${\\dot{x}}=Ax+b^{\\pm }$$\n                \n               which are ubiquitous in control theory. For this class of systems, we show the occurrence of two distinct types of Hopf-like bifurcations, each of which gives rise to a crossing limit cycle (CLC). Conditions on the system parameters for the coexistence of two CLCs and the occurrence of a saddle-node bifurcation of these CLCs are provided. Furthermore, the local asymptotic stability of the pseudo-equilibrium point is analyzed and applications in discontinuous control systems are presented.",{"EN":680},"Hopf-Like Bifurcations and Asymptotic Stability in a Class of 3D Piecewise Linear Systems with Applications",{"VOID":682},"10.1007\u002Fs00332-021-09724-2","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00332-021-09724-2",[685,702,714],{"id":686,"sortIndex":167,"researcher":22,"roles":687,"affiliations":688,"properties":699},"6ae032e7-e868-4323-859f-3dfb28db5bdb",[169],[689],{"id":22,"sortIndex":23,"affiliation":690,"properties":22},{"id":691,"createTime":692,"updateTime":693,"relativeEntities":694,"slug":695,"properties":696,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"6f40ebc6-1b69-4e5b-9240-2e0a4f0a6a29","2024-01-13T01:30:29.866+00:00","2024-10-11T00:16:33.675+00:00",[],"Institute-of-Mathematics-and-Statistics-Federal-University-of-Goi%C3%A1s-Goi%C3%A2nia-Brazil",{"title":697},{"VI":698},"Institute of Mathematics and Statistics, Federal University of Goiás, Goiânia, Brazil",{"title":700},{"VI":701},"Durval J. Tonon",{"id":703,"sortIndex":23,"researcher":22,"roles":704,"affiliations":705,"properties":711},"d3f18f9d-d214-42f2-99ac-57685b83982a",[169],[706],{"id":22,"sortIndex":23,"affiliation":707,"properties":22},{"id":691,"createTime":692,"updateTime":693,"relativeEntities":708,"slug":695,"properties":709,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},[],{"title":710},{"VI":698},{"title":712},{"VI":713},"Rony Cristiano",{"id":715,"sortIndex":376,"researcher":22,"roles":716,"affiliations":717,"properties":723},"fe084cc4-e2a4-41bc-bddc-6271a3a4c75d",[169],[718],{"id":22,"sortIndex":23,"affiliation":719,"properties":22},{"id":691,"createTime":692,"updateTime":693,"relativeEntities":720,"slug":695,"properties":721,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},[],{"title":722},{"VI":698},{"title":724},{"VI":725},"Mariana Q. Velter",{"url":683,"publisher":727,"properties":756},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":728,"slug":10,"properties":729,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":734,"manageAffiliations":735,"indexDatabases":736,"url":22,"thumbnailPath":22,"statistic":751,"gsStatistic":22,"type":140,"analyzePriority":22},[],{"issn":730,"eissn":731,"title":732,"url":733},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},[],[],[737,744],{"id":95,"indexDatabase":738,"url":108,"indexYears":109,"academicFieldIds":743,"indexDatabaseRanking":114},{"id":97,"createTime":98,"updateTime":99,"relativeEntities":739,"label":740,"description":741,"key":105,"publicationTags":742,"standard":22},[],{"EN":102,"VI":102},{"EN":102,"VI":104},[107],[111,112,113],{"id":74,"indexDatabase":745,"url":89,"indexYears":22,"academicFieldIds":750,"indexDatabaseRanking":22},{"id":76,"createTime":77,"updateTime":78,"relativeEntities":746,"label":747,"description":748,"key":85,"publicationTags":749,"standard":22},[],{"EN":81,"VI":81},{"VI":83,"EN":84},[87,88],[91,92,93],{"impactFactor":23,"impactFactorByYear":752,"i10Index":23,"i10IndexLast5Year":23,"totalPublication":117,"totalPublicationByYear":753,"totalCitation":23,"totalCitationByYear":754,"totalCitationPerPublication":23,"totalCitationPerPublicationByYear":755,"hindexLast5Year":23,"hindex":23},{},{"1991":69,"1992":119,"1993":120,"1994":121,"1995":122,"1996":123,"1997":124,"1998":122,"1999":122,"2000":125,"2001":126,"2002":69,"2003":120,"2004":122,"2005":125,"2006":69,"2007":127,"2008":123,"2009":120,"2010":121,"2011":122,"2012":128,"2013":127,"2014":129,"2015":130,"2016":131,"2017":132,"2018":131,"2019":133,"2020":134,"2021":135,"2022":136,"2023":137,"2024":123},{},{},{"volume":757,"pages":759},{"VOID":758},"31",{"VOID":760},"1-37","2021-05-25",2021,{"id":764,"createTime":765,"updateTime":766,"relativeEntities":767,"slug":768,"properties":769,"entityType":160,"verifyStatus":161,"verifyTime":766,"verifyNote":162,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":778,"fullTextUrl":22,"authors":779,"publicationType":210,"publisherRelationship":850,"citationCount":22,"citationInfo":22,"publishDate":885,"publishYear":886,"citationAnalyzeStatus":21,"lastCitationAnalyze":22,"indexDatabases":22,"openAccess":22,"references":22,"isForceReanalyzing":248},"342e2f91-ab50-4b78-a6d6-922e10ba7eba","2024-01-26T20:25:15.944+00:00","2025-02-02T23:49:19.598+00:00",[],"Phase-Transitions-and-Macroscopic-Limits-in-a-BGK-Model-of-Body-Attitude-Coordination",{"references":770,"abstract":772,"title":774,"doi":776},{"VOID":771},"Albi, G., Bellomo, N., Fermo, L., Kim, J., Pareschi, L., Poyato, D., Soler, J., et al.: Vehicular traffic, crowds, and swarms: from kinetic theory and multiscale methods to applications and research perspectives. Math. Models Methods Appl. Sci. 29(10), 1901–2005 (2019)\nBall, J.M.: Mathematics and liquid crystals. Mol. Cryst. Liq. Cryst. 647(1), 1–27 (2017)\nBall, J.M., Majumdar, A.: Nematic liquid crystals: from Maier–Saupe to a continuum theory. Mol. Cryst. Liq. Cryst. 525(1), 1–11 (2010)\nBhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94(3), 511 (1954)\nBolley, F., Canizo, J.A., Carrillo, J.A.: Stochastic mean-field limit: non-Lipschitz forces and swarming. Math. Models Methods Appl. Sci. 21(11), 2179–2210 (2011)\nBolley, F., Cañizo, J.A., Carrillo, J.A.: Mean-field limit for the stochastic Vicsek model. Appl. Math. Lett. 25(3), 339–343 (2012)\nCaflisch, R.E.: The fluid dynamic limit of the nonlinear Boltzmann equation. Comm. Pure Appl. Math. 33(5), 651–666 (1980)\nCarrillo, J.A., Choi, Y.-P., Perez, S.P.: A review on attractive-repulsive hydrodynamics for consensus in collective behavior. In: Bellomo, N., Degond, P., Tadmor, E. (eds.) Active Particles, vol. 1, pp. 259–298. Springer, Berlin (2017)\nCercignani, C., Illner, R., Pulvirenti, M.: The Mathematical Theory of Dilute Gases, vol. 106. Springer, Berlin (2013)\nChuang, Y.-L., D’Orsogna, M.R., Marthaler, D., Bertozzi, A.L., Chayes, L.S.: State transitions and the continuum limit for a 2d interacting, self-propelled particle system. Phys. D 232(1), 33–47 (2007)\nCucker, F., Smale, S.: Emergent behavior in flocks. IEEE Trans. Autom. Control 52(5), 852–862 (2007)\nDegond, P.: Macroscopic limits of the Boltzmann equation: a review. In: Degond, P., Pareschi, L., Russo, G. (eds.) Modeling and Computational Methods for Kinetic Equations, pp. 3–57. Springer, Berlin (2004)\nDegond, P., Motsch, S.: Continuum limit of self-driven particles with orientation interaction. Math. Models Methods Appl. Sci. 18(supp01), 1193–1215 (2008)\nDegond, P., Motsch, S.: A macroscopic model for a system of swarming agents using curvature control. J. Stat. Phys. 143(4), 685–714 (2011)\nDegond, P., Navoret, L.: A multi-layer model for self-propelled disks interacting through alignment and volume exclusion. Math. Models Methods Appl. Sci. 25(13), 2439–2475 (2015)\nDegond, P., Frouvelle, A., Liu, J.-G.: Macroscopic limits and phase transition in a system of self-propelled particles. J. Nonlinear Sci. 23(3), 427–456 (2013)\nDegond, P., Frouvelle, A., Liu, J.-G.: Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics. Arch. Ration. Mech. Anal. 216(1), 63–115 (2015)\nDegond, P., Frouvelle, A., Merino-Aceituno, S.: A new flocking model through body attitude coordination. Math. Models Methods Appl. Sci. 27(06), 1005–1049 (2017)\nDegond, P., Frouvelle, A., Merino-Aceituno, S., Trescases, A.: Alignment of self-propelled rigid bodies: from particle systems to macroscopic equations. arXiv preprint arXiv:1810.06903 (2018a)\nDegond, P., Frouvelle, A., Merino-Aceituno, S., Trescases, A.: Quaternions in collective dynamics. Multiscale Model. Simul. 16(1), 28–77 (2018b)\nDegond, P., Frouvelle, A., Merino-Aceituno, S., Trescases, A.: Hyperbolicity of SOHB Models (2020)\nDiez, A.: Propagation of chaos and moderate interaction for a piecewise deterministic system of geometrically enriched particles. arXiv preprint arXiv:1908.00293 (2019)\nDimarco, G., Motsch, S.: Self-alignment driven by jump processes: macroscopic limit and numerical investigation. Math. Models Methods Appl. Sci. 26(07), 1385–1410 (2016)\nEsposito, R., Guo, Y., Kim, C., Marra, R.: Stationary solutions to the Boltzmann equation in the hydrodynamic limit. Ann. PDE 4(1), 1 (2018)\nFigalli, A., Kang, M.-J., Morales, J.: Global well-posedness of the spatially homogeneous Kolmogorov–Vicsek model as a gradient flow. Arch. Ration. Mech. Anal. 227(3), 869–896 (2018)\nGallagher, I., Saint-Raymond, L., Texier, B.: From Newton to Boltzmann: hard spheres and short-range potentials. Zürich lectures in advanced mathematics. European Mathematical Society (2013). ISBN: 9783037191293\nGamba, I.M., Kang, M.-J.: Global weak solutions for Kolmogorov–Vicsek type equations with orientational interactions. Arch. Ration. Mech. Anal. 222(1), 317–342 (2016)\nGiacomin, G., Pakdaman, K., Pellegrin, X.: Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators. Nonlinearity 25(5), 1247 (2012a)\nGiacomin, G., Pakdaman, K., Pellegrin, X., Poquet, C.: Transitions in active rotator systems: invariant hyperbolic manifold approach. SIAM J. Math. Anal. 44(6), 4165–4194 (2012b)\nGolse, F., Saint-Raymond, L.: The Navier–Stokes limit of the Boltzmann equation for bounded collision kernels. Invent. Math. 155(1), 81–161 (2004)\nGuo, Y., Jang, J.: Global Hilbert expansion for the Vlasov–Poisson–Boltzmann system. Commun. Math. Phys. 299(2), 469–501 (2010)\nHa, S.-Y., Liu, J.-G., et al.: A simple proof of the Cucker–Smale flocking dynamics and mean-field limit. Commun. Math. Sci. 7(2), 297–325 (2009)\nHan, J., Luo, Y., Wang, W., Zhang, P., Zhang, Z.: From microscopic theory to macroscopic theory: a systematic study on modeling for liquid crystals. Arch. Ration. Mech. Anal. 215(3), 741–809 (2015)\nHaragus, M., Iooss, G.: Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems. Springer, Berlin (2010)\nHaraux, A.: Some applications of the Łojasiewicz gradient inequality. Commun. Pure Appl. Anal. 6, 2417–2427 (2012)\nHauray, M., Jabin, P.-E.: N-particles approximation of the Vlasov equations with singular potential. Arch. Ration. Mech. Anal. 183(3), 489–524 (2007)\nHemelrijk, C.K., Hildenbrandt, H.: Schools of fish and flocks of birds: their shape and internal structure by self-organization. Interface Focus 2(6), 726–737 (2012)\nHemelrijk, C.K., Hildenbrandt, H., Reinders, J., Stamhuis, E.J.: Emergence of oblong school shape: models and empirical data of fish. Ethology 116(11), 1099–1112 (2010)\nHildenbrandt, H., Carere, C., Hemelrijk, C.K.: Self-organized aerial displays of thousands of starlings: a model. Behav. Ecol. 21(6), 1349–1359 (2010)\nHirsch, M.W., Smale, S., Devaney, R.L.: Differential Equations, Dynamical Systems, and an Introduction to Chaos. Academic Press, London (2012)\nHorn, A.: Doubly stochastic matrices and the diagonal of a rotation matrix. Am. J. Math. 76(3), 620–630 (1954)\nJabin, P.-E.: A review of the mean field limits for Vlasov equations. Kinet. Relat. Models 7(4), 661–711 (2014)\nJiang, N., Xiong, L., Zhang, T.-F.: Hydrodynamic limits of the kinetic self-organized models. SIAM J. Math. Anal. 48(5), 3383–3411 (2016)\nJiang, N., Luo, Y.-L., Zhang, T.-F.: Coupled self-organized hydrodynamics and Navier–Stokes models: local well-posedness and the limit from the self-organized kinetic-fluid models. arXiv preprint arXiv:1712.10134 (2017)\nJourdain, B., Méléard, S.: Propagation of chaos and fluctuations for a moderate model with smooth initial data. Ann. Inst. Henri Poincaré Probab. Stat. 34(6), 727–766 (1998)\nKac, M.: Foundations of kinetic theory. In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. 3, pp. 171–197. University of California Press Berkeley and Los Angeles, CA (1956)\nLanford, O.E.: Time evolution of large classical systems. In: Moser, J. (ed.) Dynamical Systems, Theory and Applications, pp. 1–111. Springer, Berlin (1975)\nLax, P.D.: Linear Algebra and Its Applications, 2nd edn. Wiley, New York (2007)\nŁojasiewicz, S.: Sur les trajectoires du gradient d’une fonction analytique. Seminari di geometria, Univ. Stud. Bologna, Bologna 1982–1983, 115–117 (1984)\nMarchetti, M.C., Joanny, J.F., Ramaswamy, S., Liverpool, T.B., Prost, J., Rao, M., Simha, R.A.: Hydrodynamics of soft active matter. Rev. Mod. Phys. 85(3), 1143–1189 (2013)\nMischler, S., Mouhot, C.: Kac’s program in kinetic theory. Invent. Math. 193(1), 1–147 (2013)\nMorales, J., Poyato, D.: On the trend to global equilibrium for Kuramoto Oscillators. arXiv preprint arXiv:1908.07657 (2019)\nMotsch, S., Tadmor, E.: A new model for self-organized dynamics and its flocking behavior. J. Stat. Phys. 144(5), 923 (2011)\nOelschläger, K.: A law of large numbers for moderately interacting diffusion processes. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 69(2), 279–322 (1985)\nPerko, L.: Differential Equations and Dynamical Systems, vol. 7. Springer, Berlin (2013)\nPerthame, B.: Global existence to the BGK model of Boltzmann equation. J. Differ. Equ. 82, 191–205 (1989)\nQuarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics, vol. 37. Springer, Berin (2010)\nSaint-Raymond, L.: From the BGK model to the Navier–Stokes equations. Ann. Sci. Éc. Norm. Supér. 36(4), 271–317 (2003)\nSalamin, E.: Application of quaternions to computation with rotations. Technical report, Working Paper (1979)\nSznitman, A.-S.: Topics in propagation of chaos. In: Hennequin, P.-L. (ed.) Éc. Été Probab. St.-Flour XIX—1989, pp. 165–251. Springer, Berlin (1991)\nVicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75(6), 1226 (1995)\nWang, H., Hoffman, P., et al.: A unified view on the rotational symmetry of equilibiria of nematic polymers, dipolar nematic polymers, and polymers in higher dimensional space. Commun. Math. Sci. 6(4), 949–974 (2008)\nZhang, T.-F., Jiang, N.: A local existence of viscous self-organized hydrodynamic model. Nonlinear Anal. Real World Appl. 34, 495–506 (2017)\nZhou, H., Wang, H.: Stability of equilibria of nematic liquid crystalline polymers. Acta Math. Sci. 31(6), 2289–2304 (2011)",{"EN":773},"In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body attitude of an agent is modelled by a rotation matrix in \n$${\\mathbb {R}}^3$$\n\n as in Degond et al. (Math Models Methods Appl Sci 27(6):1005–1049, 2017). The starting point of this study is a BGK equation modelling the evolution of the distribution function of the system at a kinetic level. The main novelty of this work is to show that in the spatially homogeneous case, self-organisation may appear or not depending on the local density of agents involved. We first exhibit a connection between body-orientation models and models of nematic alignment of polymers in higher-dimensional space from which we deduce the complete description of the possible equilibria. Then, thanks to a gradient-flow structure specific to this BGK model, we are able to prove the stability and the convergence towards the equilibria in the different regimes. We then derive the macroscopic models associated with the stable equilibria in the spirit of Degond et al. (Arch Ration Mech Anal 216(1):63–115, 2015, Math Models Methods Appl Sci 27(6):1005–1049, 2017).\n",{"EN":775},"Phase Transitions and Macroscopic Limits in a BGK Model of Body-Attitude Coordination",{"VOID":777},"10.1007\u002Fs00332-020-09632-x","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00332-020-09632-x",[780,805,822,838],{"id":781,"sortIndex":577,"researcher":22,"roles":782,"affiliations":783,"properties":802},"32ed6712-2eca-4b9b-92aa-d3b8ee27543c",[169],[784,794],{"id":785,"sortIndex":167,"affiliation":786,"properties":793},"636f4e2a-9e43-4998-929b-f90fdbda71e9",{"id":787,"createTime":788,"updateTime":788,"relativeEntities":789,"slug":22,"properties":790,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"9e01f010-84a9-4d5d-a63b-0a580d76f46d","2024-02-14T05:11:07.896+00:00",[],{"title":791},{"VI":792},"Department of Mathematics, University of Sussex, Falmer, UK",{},{"id":22,"sortIndex":23,"affiliation":795,"properties":22},{"id":796,"createTime":797,"updateTime":797,"relativeEntities":798,"slug":22,"properties":799,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"562ad4d6-099c-4d74-b528-2de26b47ba36","2023-12-27T09:30:37.665+00:00",[],{"title":800},{"VI":801},"Faculty of Mathematics, University of Vienna, Wien, Austria",{"title":803},{"VI":804},"S. Merino-Aceituno",{"id":806,"sortIndex":167,"researcher":22,"roles":807,"affiliations":808,"properties":819},"838a3db0-b68c-4df7-872e-acdf4532861f",[169],[809],{"id":22,"sortIndex":23,"affiliation":810,"properties":22},{"id":811,"createTime":812,"updateTime":813,"relativeEntities":814,"slug":815,"properties":816,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"a9cf47a3-a935-4ef5-a845-0a102fc7bfd1","2024-01-05T19:28:36.259+00:00","2024-11-28T15:46:15.906+00:00",[],"Department-of-Mathematics-Imperial-College-London-London-UK",{"title":817},{"VI":818},"Department of Mathematics, Imperial College London, London , UK",{"title":820},{"VI":821},"A. Diez",{"id":823,"sortIndex":376,"researcher":22,"roles":824,"affiliations":825,"properties":835},"5811ffe1-5b48-4f4c-aa2c-cde2c8e4efc9",[169],[826],{"id":22,"sortIndex":23,"affiliation":827,"properties":22},{"id":828,"createTime":829,"updateTime":829,"relativeEntities":830,"slug":831,"properties":832,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"1f13796c-701b-41e2-bba4-1e2e44247ee8","2024-04-06T16:01:03.075+00:00",[],"CEREMADE-CNRS-Universit%C3%A9-Paris-Dauphine-Universit%C3%A9-PSL-Paris-France",{"title":833},{"VI":834},"CEREMADE, CNRS, Université Paris-Dauphine, Université PSL, Paris, France",{"title":836},{"VI":837},"A. Frouvelle",{"id":839,"sortIndex":23,"researcher":22,"roles":840,"affiliations":841,"properties":847},"e94461f9-6ae1-44d1-9709-f5c57e750e77",[169],[842],{"id":22,"sortIndex":23,"affiliation":843,"properties":22},{"id":811,"createTime":812,"updateTime":813,"relativeEntities":844,"slug":815,"properties":845,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},[],{"title":846},{"VI":818},{"title":848},{"VI":849},"P. Degond",{"url":778,"publisher":851,"properties":880},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":852,"slug":10,"properties":853,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":858,"manageAffiliations":859,"indexDatabases":860,"url":22,"thumbnailPath":22,"statistic":875,"gsStatistic":22,"type":140,"analyzePriority":22},[],{"issn":854,"eissn":855,"title":856,"url":857},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},[],[],[861,868],{"id":95,"indexDatabase":862,"url":108,"indexYears":109,"academicFieldIds":867,"indexDatabaseRanking":114},{"id":97,"createTime":98,"updateTime":99,"relativeEntities":863,"label":864,"description":865,"key":105,"publicationTags":866,"standard":22},[],{"EN":102,"VI":102},{"EN":102,"VI":104},[107],[111,112,113],{"id":74,"indexDatabase":869,"url":89,"indexYears":22,"academicFieldIds":874,"indexDatabaseRanking":22},{"id":76,"createTime":77,"updateTime":78,"relativeEntities":870,"label":871,"description":872,"key":85,"publicationTags":873,"standard":22},[],{"EN":81,"VI":81},{"VI":83,"EN":84},[87,88],[91,92,93],{"impactFactor":23,"impactFactorByYear":876,"i10Index":23,"i10IndexLast5Year":23,"totalPublication":117,"totalPublicationByYear":877,"totalCitation":23,"totalCitationByYear":878,"totalCitationPerPublication":23,"totalCitationPerPublicationByYear":879,"hindexLast5Year":23,"hindex":23},{},{"1991":69,"1992":119,"1993":120,"1994":121,"1995":122,"1996":123,"1997":124,"1998":122,"1999":122,"2000":125,"2001":126,"2002":69,"2003":120,"2004":122,"2005":125,"2006":69,"2007":127,"2008":123,"2009":120,"2010":121,"2011":122,"2012":128,"2013":127,"2014":129,"2015":130,"2016":131,"2017":132,"2018":131,"2019":133,"2020":134,"2021":135,"2022":136,"2023":137,"2024":123},{},{},{"volume":881,"pages":883},{"VOID":882},"30",{"VOID":884},"2671-2736","2020-05-30",2020,{"id":888,"createTime":889,"updateTime":889,"relativeEntities":890,"slug":22,"properties":891,"entityType":160,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":900,"fullTextUrl":22,"authors":901,"publicationType":210,"publisherRelationship":956,"citationCount":22,"citationInfo":22,"publishDate":990,"publishYear":762,"citationAnalyzeStatus":21,"lastCitationAnalyze":22,"indexDatabases":22,"openAccess":22,"references":22,"isForceReanalyzing":248},"121cbde1-7e28-46a1-bb14-9d6b8ea20a30","2023-12-05T23:49:02.241+00:00",[],{"references":892,"abstract":894,"title":896,"doi":898},{"VOID":893},"Bertsch, M., Gurtin, M., Hilhorst, D., Peletier, L.: On interacting populations that disperse to avoid crowding: preservation of segregation. J. Math. Biol. 23, 1–13 (1985)\nBurger, M., Carrillo, J.A., Pietschmann, J.-F., Schmidtchen, M.: Segregation effects and gap formation in cross-diffusion models. Interfaces Free Bound. 22, 175–203 (2020a)\nBurger, M., Pietschmann, J.-F., Ranetbauer, H., Schmeiser, C., Wolfram, M.-T.: Mean-field models for segregation dynamics. Eur. J. Appl. Math. To appear in arXiv:1808.04069 (2020b)\nChen, L., Göttlich, S., Knapp, S.: Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation. ESAIM: Math. Mod. Num. Anal. 53, 567–593 (2018a)\nChen, X., Daus, E.S., Jüngel, A.: Global existence analysis of cross-diffusion population systems for multiple species. Arch. Ration. Mech. Anal. 227, 715–747 (2018b)\nChen, L., Daus, E.S., Jüngel, A.: Rigorous mean-field limits and cross diffusion. Z. Angew. Math. Phys. 70(122), 21 (2019)\nDaus, E.S., Desvillettes, L., Dietert, H.: About the entropic structure of detailed balanced multi-species cross-diffusion equations. J. Differ. Equ. 266, 3861–3882 (2019)\nDaus, E.S., Ptashnyk, M., Raithel, C.: Derivation of a fractional cross-diffusion system as the limit of a stochastic many-particle system driven by Lévy noise. Submitted for publication. arXiv:2006.00277 (2020)\nDesvillettes, L., Lepoutre, T., Moussa, A., Trescases, A.: On the entropic structure of reaction-cross-diffusion systems. Commun. Partial Differ. Equ. 40, 1705–1747 (2015)\nFigalli, A., Philipowski, R.: Convergence to the viscous porous medium equation and propagation of chaos. Alea 4, 185–203 (2008)\nFontbona, J., Méléard, S.: Non local Lotka–Volterra system with cross-diffusion in an heterogeneous medium. J. Math. Biol. 70, 829–854 (2015)\nGolse, F.: The mean-field limit for the dynamics of large particle systems. Journées Equations aux dérivées partielles 1–47 (2003)\nIchikawa, K., Rouzimaimaiti, M., Suzuki, T.: Reaction diffusion equation with non-local term arises as a mean field limit of the master equation. Discrete Cont. Dyn. Syst. Ser. S 5, 115–126 (2012)\nJabin, P.-E., Wang, Z.: Mean field limit for stochastic particle systems. In: Active Particles, Vol. 1, pp. 379–402. Springer, Boston (2017)\nJourdain, B., Méléard, S.: Propagation of chaos and fluctuations for a moderate model with smooth initial data. Ann. Inst. H. Poincaré Probab. Stat. 34, 727–766 (1998)\nKaratzas, I., Shreve, S.: Brownian Motion and Stochastic Calculus, 2nd edn. Springer, New York (1991)\nKloeden, P., Platen, E.: Numerical Solution of Stochastic Differential Equations. Springer, Berlin (1992)\nLepoutre, T., Moussa, A.: Entropic structure and duality for multiple species cross-diffusion systems. Nonlinear Anal. 159, 298–315 (2017)\nLieb, E.H., Loss, M.: Analysis, 2nd edn. American Mathematical Society, Providence (2001)\nMajda, A.: Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Springer, New York (1984)\nMoussa, A.: From non-local to classical SKT systems: triangular case with bounded coefficients. SIAM J. Math. Anal. 52, 42–64 (2020)\nNualart, D.: The Malliavin Calculus and Related Topics. Springer, Berlin (2006)\nOelschläger, K.: A martingale approach to the law of large numbers for weakly interacting stochastic processes. Ann. Prob. 12, 458–479 (1984)\nOelschläger, K.: On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes. Prob. Theory Relat. Fields 82, 565–586 (1989)\nOelschläger, K.: Large systems of interacting particles and the porous medium equation. J. Differ. Equ. 88, 294–346 (1990)\nSeo, I.: Scaling limit of two-component interacting Brownian motions. Ann. Prob. 46, 2038–2063 (2018)\nShigesada, N., Kawasaki, K., Teramoto, E.: Spatial segregation of interacting species. J. Theor. Biol. 79, 83–99 (1979)\nStevens, A.: The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems. SIAM J. Appl. Math. 61, 183–212 (2000). (Erratum: 61 (2000), 2200-2200.)\nSznitman, A.S.: Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated. J. Funct. Anal. 56, 311–336 (1984)\nSznitman, A.S.: Topics in propagation of chaos. In: P.L. Hennequin (ed.), École d’Été de Probabilités de Saint-Flour XIX-1989, Lecture Notes Mathematics 1464. Berlin, Springer (1991)\nZamponi, N., Jüngel, A.: Analysis of degenerate cross-diffusion population models with volume filling. Ann. Inst. H. Poincaré Anal. Nonlinear 34, 1–29 (2017)",{"EN":895},"Population cross-diffusion systems of Shigesada–Kawasaki–Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion term in the stochastic model depends nonlinearly on the interactions between the individuals, and the drift term is the gradient of the environmental potential. In the first step, the mean-field limit leads to an intermediate nonlocal model. The local cross-diffusion system is derived in the second step in a moderate scaling regime, when the interaction potentials approach the Dirac delta distribution. The global existence of strong solutions to the intermediate and the local diffusion systems is proved for sufficiently small initial data. Furthermore, numerical simulations on the particle level are presented.",{"EN":897},"Rigorous Derivation of Population Cross-Diffusion Systems from Moderately Interacting Particle Systems",{"VOID":899},"10.1007\u002Fs00332-021-09747-9","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs00332-021-09747-9",[902,917,929,944],{"id":903,"sortIndex":577,"researcher":22,"roles":904,"affiliations":905,"properties":914},"441d8df9-b0ad-47d8-97f5-c00201161ba4",[169],[906],{"id":22,"sortIndex":23,"affiliation":907,"properties":22},{"id":908,"createTime":909,"updateTime":909,"relativeEntities":910,"slug":22,"properties":911,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"43a78248-9322-420f-83e6-113fd5057e7f","2024-02-21T22:19:41.394+00:00",[],{"title":912},{"VI":913},"Institute of Analysis and Scientific Computing, TU Wien, Vienna, Austria",{"title":915},{"VI":916},"Ansgar Jüngel",{"id":918,"sortIndex":376,"researcher":22,"roles":919,"affiliations":920,"properties":926},"932c9559-5165-423a-8193-509042553526",[169],[921],{"id":22,"sortIndex":23,"affiliation":922,"properties":22},{"id":908,"createTime":909,"updateTime":909,"relativeEntities":923,"slug":22,"properties":924,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},[],{"title":925},{"VI":913},{"title":927},{"VI":928},"Alexandra Holzinger",{"id":930,"sortIndex":23,"researcher":22,"roles":931,"affiliations":932,"properties":941},"945bbc9f-81a4-463e-a9be-58b232d6bd2e",[169],[933],{"id":22,"sortIndex":23,"affiliation":934,"properties":22},{"id":935,"createTime":936,"updateTime":936,"relativeEntities":937,"slug":22,"properties":938,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"527d72b5-cf20-4015-aa39-000ec560c6ce","2023-12-11T11:17:09.569+00:00",[],{"title":939},{"VI":940},"School of Business Informatics and Mathematics, University of Mannheim, Mannheim, Germany",{"title":942},{"VI":943},"Li Chen",{"id":945,"sortIndex":167,"researcher":22,"roles":946,"affiliations":947,"properties":953},"e310ee19-4146-4851-a3cb-c5938d7b8f34",[169],[948],{"id":22,"sortIndex":23,"affiliation":949,"properties":22},{"id":908,"createTime":909,"updateTime":909,"relativeEntities":950,"slug":22,"properties":951,"entityType":58,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},[],{"title":952},{"VI":913},{"title":954},{"VI":955},"Esther S. Daus",{"url":900,"publisher":957,"properties":986},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":958,"slug":10,"properties":959,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":964,"manageAffiliations":965,"indexDatabases":966,"url":22,"thumbnailPath":22,"statistic":981,"gsStatistic":22,"type":140,"analyzePriority":22},[],{"issn":960,"eissn":961,"title":962,"url":963},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},[],[],[967,974],{"id":95,"indexDatabase":968,"url":108,"indexYears":109,"academicFieldIds":973,"indexDatabaseRanking":114},{"id":97,"createTime":98,"updateTime":99,"relativeEntities":969,"label":970,"description":971,"key":105,"publicationTags":972,"standard":22},[],{"EN":102,"VI":102},{"EN":102,"VI":104},[107],[111,112,113],{"id":74,"indexDatabase":975,"url":89,"indexYears":22,"academicFieldIds":980,"indexDatabaseRanking":22},{"id":76,"createTime":77,"updateTime":78,"relativeEntities":976,"label":977,"description":978,"key":85,"publicationTags":979,"standard":22},[],{"EN":81,"VI":81},{"VI":83,"EN":84},[87,88],[91,92,93],{"impactFactor":23,"impactFactorByYear":982,"i10Index":23,"i10IndexLast5Year":23,"totalPublication":117,"totalPublicationByYear":983,"totalCitation":23,"totalCitationByYear":984,"totalCitationPerPublication":23,"totalCitationPerPublicationByYear":985,"hindexLast5Year":23,"hindex":23},{},{"1991":69,"1992":119,"1993":120,"1994":121,"1995":122,"1996":123,"1997":124,"1998":122,"1999":122,"2000":125,"2001":126,"2002":69,"2003":120,"2004":122,"2005":125,"2006":69,"2007":127,"2008":123,"2009":120,"2010":121,"2011":122,"2012":128,"2013":127,"2014":129,"2015":130,"2016":131,"2017":132,"2018":131,"2019":133,"2020":134,"2021":135,"2022":136,"2023":137,"2024":123},{},{},{"volume":987,"pages":988},{"VOID":758},{"VOID":989},"1-38","2021-09-28",{"id":992,"createTime":993,"updateTime":994,"relativeEntities":995,"slug":996,"properties":997,"entityType":160,"verifyStatus":21,"verifyTime":994,"verifyNote":529,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":1006,"fullTextUrl":22,"authors":1007,"publicationType":210,"publisherRelationship":1060,"citationCount":22,"citationInfo":22,"publishDate":1095,"publishYear":1096,"citationAnalyzeStatus":21,"lastCitationAnalyze":22,"indexDatabases":22,"openAccess":22,"references":22,"isForceReanalyzing":248},"68b6660d-a888-4bf5-88dc-b98469d7a34b","2024-01-10T17:23:05.971+00:00","2024-12-14T23:47:10.018+00:00",[],"Complex-Valued-Burgers-and-KdV-Burgers-Equations",{"references":998,"abstract":1000,"title":1002,"doi":1004},{"VOID":999},"Birnir, B.: An example of blow-up, for the complex KdV equation and existence beyond the blow-up. SIAM J. Appl. Math. 47, 710–725 (1987)\nBona, J.L., Weissler, F.B.: Blow up of spatially periodic complex-valued solutions of nonlinear dispersive equations. Indiana Univ. Math. J. 50, 759–782 (2001)\nHardy, G.H., Ramanujan, S.: Asymptotic formulae in combinatory analysis. Proc. Lond. Math. Soc. 17, 75–115 (1918)\nKenyon, R., Okounkov, A.: Limit shapes and the complex Burgers equation. Acta Math. 199, 263–302 (2007)\nKerszberg, M.: A simple model for unidirectional crystal growth. Phys. Lett. A 105, 241–244 (1984)\nLevi, D.: Levi-Civita theory for irrotational water waves in a one-dimensional channel and the complex Korteweg–de Vries equation. Teor. Mat. Fiz. 99, 435–440 (1994); translation in Theor. Math. Phys. 99, 705–709 (1994)\nLevi, D., Sanielevici, M.: Irrotational water waves and the complex Korteweg–de Vries equation. Physica D 98, 510–514 (1996)\nLi, Y.C.: Simple explicit formulae for finite time blow up solutions to the complex KdV equation. Chaos Solitons Fractals 39, 369–372 (2009)\nLi, D., Sinai, Y.: Blow ups of complex solutions of the 3D Navier–Stokes system and renormalization group method. J. Eur. Math. Soc. 10, 267–313 (2008)\nLiu, T., Zumbrun, K.: Nonlinear stability of an undercompressive shock for complex Burgers equation. Commun. Math. Phys. 168, 163–186 (1995)\nPoláčik, P., Šverák, V.: Zeros of complex caloric functions and singularities of complex viscous Burgers equation. J. Reine Angew. Math. 616, 205–217 (2008)\nWu, J., Yuan, J.-M.: The effect of dissipation on solutions of the complex KdV equation. Math. Comput. Simul. 69, 589–599 (2005)\nWu, J., Yuan, J.-M.: Local well-posedness and local (in space) regularity results for the complex Korteweg–de Vries equation. Proc. R. Soc. Edinb. A 137, 203–223 (2007)\nYuan, J.-M., Wu, J.: The complex KdV equation with or without dissipation. Discrete Contin. Dyn. Syst., Ser. B 5, 489–512 (2005)",{"EN":1001},"Spatially periodic complex-valued solutions of the Burgers and KdV–Burgers equations are studied in this paper. It is shown that for any sufficiently large time T, there exists an explicit initial datum such that its corresponding solution of the Burgers equation blows up at T. 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