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Motivated by the achievements from both the stability of neural networks with time delay in the leakage term and the synchronization of coupled chaotic fuzzy cellular neural networks with stochastic perturbation, Lyapunov stability theory combining with stochastic analysis approaches are employed to derive sufficient criteria ensuring the coupled chaotic fuzzy cellular neural networks to be completely synchronous. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.",{"EN":128},"Synchronization of Stochastic Fuzzy Cellular Neural Networks with Leakage Delay Based on Adaptive Control",{"VOID":130},"10.1007\u002Fs12591-013-0189-z",{"VOID":132},"[\"14404665441972658413\"]","PUBLICATION","VERIFIED","2024-04-30T10:07:25.308+00:00","Auto Verify","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs12591-013-0189-z",[139,156,169,181],{"id":140,"sortIndex":109,"researcher":20,"roles":141,"affiliations":143,"properties":153},"69af35ab-deb9-428f-bc10-33400fa045a3",[142],"AUTHOR",[144],{"id":20,"sortIndex":21,"affiliation":145,"properties":20},{"id":146,"createTime":147,"updateTime":147,"relativeEntities":148,"slug":149,"properties":150,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"bb06b8ce-c9e5-40a4-a00d-0957f8a9ed37","2023-11-29T11:42:53.558+00:00",[],"Department-of-Basic-Science-Shijiazhuang-Mechanical-Engineering-College-Shijiazhuang-People-s-Republic-of-China",{"title":151},{"VI":152},"Department of Basic Science, Shijiazhuang Mechanical Engineering College, Shijiazhuang, People’s Republic of China",{"title":154},{"VI":155},"Yuzhong Yang",{"id":157,"sortIndex":158,"researcher":20,"roles":159,"affiliations":160,"properties":166},"0e43176c-a406-4e9d-8b69-dc13be301ac0",3,[142],[161],{"id":20,"sortIndex":21,"affiliation":162,"properties":20},{"id":146,"createTime":147,"updateTime":147,"relativeEntities":163,"slug":149,"properties":164,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":165},{"VI":152},{"title":167},{"VI":168},"Yanwei Wang",{"id":170,"sortIndex":110,"researcher":20,"roles":171,"affiliations":172,"properties":178},"df975250-07bb-486c-bd33-476320cc6241",[142],[173],{"id":20,"sortIndex":21,"affiliation":174,"properties":20},{"id":146,"createTime":147,"updateTime":147,"relativeEntities":175,"slug":149,"properties":176,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":177},{"VI":152},{"title":179},{"VI":180},"Shengli Fan",{"id":182,"sortIndex":21,"researcher":20,"roles":183,"affiliations":184,"properties":190},"d1cfb6fe-0ac1-4f43-9920-fbfedd6b1cfc",[142],[185],{"id":20,"sortIndex":21,"affiliation":186,"properties":20},{"id":146,"createTime":147,"updateTime":147,"relativeEntities":187,"slug":149,"properties":188,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":189},{"VI":152},{"title":191},{"VI":192},"Qintao Gan","ARTICLE",{"url":137,"publisher":195,"properties":223},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":196,"slug":10,"properties":197,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":201,"manageAffiliations":202,"indexDatabases":203,"url":104,"thumbnailPath":20,"statistic":218,"gsStatistic":20,"type":113,"analyzePriority":20},[],{"issn":198,"eissn":199,"title":200},{"VOID":13},{"VOID":15},{"EN":17},[],[],[204,211],{"id":66,"indexDatabase":205,"url":79,"indexYears":80,"academicFieldIds":210,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":206,"label":207,"description":208,"key":76,"publicationTags":209,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"id":86,"indexDatabase":212,"url":101,"indexYears":20,"academicFieldIds":217,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":213,"label":214,"description":215,"key":97,"publicationTags":216,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"impactFactor":21,"impactFactorByYear":219,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":107,"totalPublicationByYear":220,"totalCitation":21,"totalCitationByYear":221,"totalCitationPerPublication":21,"totalCitationPerPublicationByYear":222,"hindexLast5Year":21,"hindex":21},{},{"2015":109,"2016":110,"2018":109,"2019":110,"2021":110,"2024":109},{},{},{"volume":224,"pages":226},{"VOID":225},"22",{"VOID":227},"319-332",{"total":21,"publishYear":21,"statisticByYear":229},{},"2013-11-07",2013,[233,239,242,248,251,254,260,266,269,272,275,281,284,290,296,299,302,305,308,311,314,320,323,326,332,335,338,341,344,347,353,356,359,362,365,371,374,377,380,383,389,392,395,398,401],{"id":234,"text":235,"url":236,"identifiers":237},"4c68646b-0035-4279-8000-0006b275d4fa","Coelho, L.S., Grebogi, R.B.: Chaotic synchronization using PID control combined with population based incremental learning algorithm. 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Numer. Simul. 17, 1003–1011 (2012)",{"doi":238},{"id":234,"text":303,"url":236,"identifiers":304},"Yang, T., Yang, L., Wu, C., Chua, L.O.: Fuzzy cellular neural networks: theory. In: Proceedings of IEEE International Workshop on Cellular Neural Networks and Applications, pp. 181–186 (1996)",{"doi":238},{"id":234,"text":306,"url":236,"identifiers":307},"Yang,T., Yang, L., Wu, C., Chua, L.O.: Fuzzy cellular neural networks: applications. In: Proceedings of IEEE International Workshop on Cellular Neural Networks and Applications, pp. 225–230 (1996).",{"doi":238},{"id":234,"text":309,"url":236,"identifiers":310},"Balasubramaniam, P., Vembarasan, V., Rakkiyappan, R.: Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays. Commun. Nonlinear Sci. Numer. 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Simul. 16, 4422–4437 (2011)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS1007570411001584",{"doi":388},"10.1016\u002Fj.cnsns.2011.03.028",{"id":234,"text":390,"url":236,"identifiers":391},"Balasubramaniam, P., Vembarasan, V., Rakkiyappan, R.: Leakage delays in T–S fuzzy cellular neural networks. Neural Process. Lett. 33, 111–136 (2011)",{"doi":238},{"id":234,"text":393,"url":236,"identifiers":394},"Li, C., Huang, T.: On the stability of nonlinear systems with leakage delay. J. Franklin Inst. 346, 366–377 (2009)",{"doi":238},{"id":234,"text":396,"url":236,"identifiers":397},"Gu, K.: An integral inequality in the stability problem of time-delay system. In: Processings of 39th IEEE Conference on Decision and Control, pp. 2805–2810 (2000)",{"doi":238},{"id":234,"text":399,"url":236,"identifiers":400},"Tang, Y., Fang, J.: Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling. Neurocomputing 72, 3253–3262 (2009)",{"doi":238},{"id":402,"text":403,"url":404,"identifiers":405},"c292a875-7824-4e58-8211-811234e106a4","Wang, Y., Cao, J.: Synchronization of a class of delayed neural networks with reaction–diffusion terms. Phys. Lett. A 369, 201–211 (2007)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0375960107006524",{"doi":406},"10.1016\u002Fj.physleta.2007.04.079",false,{"id":409,"createTime":410,"updateTime":411,"relativeEntities":412,"slug":413,"properties":414,"entityType":133,"verifyStatus":134,"verifyTime":411,"verifyNote":136,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":423,"fullTextUrl":20,"authors":424,"publicationType":193,"publisherRelationship":467,"citationCount":20,"citationInfo":20,"publishDate":501,"publishYear":502,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":407},"db7231e0-ed04-4c3e-90bf-8d7240545953","2024-02-14T10:43:02.911+00:00","2024-12-27T23:57:08.983+00:00",[],"Oscillation-of-third-order-nonlinear-functional-dynamic-equations-on-time-scales",{"references":415,"abstract":417,"title":419,"doi":421},{"VOID":416},"Agarwal R., Bohner M. and Saker S. H., Oscillation of second order delay dynamic equations, Canad. Appl. Math. Quart., 13, 1–17, (2005)\nBohner M. and Peterson A., Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, (2001)\nBohner M. and Peterson A., Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, (2003)\nBohner M. and Saker S. H., Oscillation of second order half-linear dynamic equations on discrete time scales, Internat. J. Difference Equs., 1, 208–218, (2006)\nGera M., Graef J. R. and Gregus M., On oscillatory and asymptotic properties of solutions of certain nonlinear third order differential equations, Nonlinear Anal., 32, 417–425, (1998)\nDošlý O. and Hilger E., A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales, Special Issue on Dynamic Equations on Time Scales (Agarwal P. P., Bohner M. and O’Regan D., eds.), J. Comp. Appl. Math., 141(1–2), 571–585, (2002)\nElabbasy E. M. and Hassan T. S., Oscillation of third order nonlinear functional differential equations, Diff. Eq. Appl., submitted\nErbe L., Hassan T. S. and Peterson A., Oscillation criteria for nonlinear damped dynamic equations on time scales, Appl. Math. Comp., 203, 343–357, (2008)\nErbe L., Hassan T. S. and Peterson A., Oscillation criteria for nonlinear functional neutral dynamic equations on time scales, J. Diff. Eq. Appl., 15, 1097–1115, (2009)\nErbe L., Hassan T. S., Peterson A. and Saker S. H., Oscillation criteria for half-linear delay dynamic equations on time scales, Nonlinear Dynam. Sys. Th., 9, 51–68, (2009)\nErbe L., Hassan T. S., Peterson A. and Saker S. H., Oscillation criteria for sublinear half-linear delay dynamic equations on time scales, Int. J. Diff. Equ., 3, 227–245, (2008)\nErbe L., Peterson A. and Saker S. H., Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales, J. Comp. Appl. Math., 181, 92–102, (2005)\nErbe L., Peterson A. and Saker S. H., Hille and Nehari type criteria for third order dynamic equations, J. Math. Anal. Appl., 329, 112–131, (2007)\nErbe L., Peterson A. and Saker S. H., Oscillation and asymptotic behavior a third-order nonlinear dynamic equation, Canad. Quart. Appl. Math., 14, 2, (2006)\nHardy G. H., Littlewood J. E. and Polya G., Inequalities, second ed., Cambridge University Press, Cambridge, (1988)\nHassan T. S., Oscillation criteria for half-linear dynamic equations on time scales, J. Math. Anal. Appl., 345, 176–185, (2008)\nHilger S., Analysis on measure chains — a unified approach to continuous and discrete calculus, Results Math., 18, 18–56, (1990)\nKac V. and Cheung P., Quantum Calculus, Universitext, (2002)\nZhang B. G. and Deng X., Oscillation of delay differential equations on time scales, Math. Comp. Mod., 36, 1307–1318, (2002)\nŞahiner Y. and Stavroulakis I. S., Oscillation of first order delay dynamic equations, Dynam. Systems Appl., 15, 645–655, (2006)\nWu H., Zhuang R. and Mathsen R. M., Oscillation criteria of second-order nonlinear neutral variable delay dynamic equations, Appl. Math. Comp., 178, 321–331, (2006)",{"EN":418},"It is the purpose of this paper to give oscillation criteria for the third order nonlinear functional dynamic equation \n                  \n                    \n                  \n                  $$\n\\left( {a\\left( t \\right)\\left[ {\\left( {r\\left( t \\right)x^\\Delta  \\left( t \\right)} \\right)^\\Delta  } \\right]^\\gamma  } \\right)^\\Delta   + f\\left( {t,x\\left( {g\\left( t \\right)} \\right)} \\right) = 0\n$$\n                 on a time scale \n                  \n                    \n                  \n                  $$\n\\mathbb{T}\n$$\n                , where γ is the quotient of odd positive integers, a and r are positive rd-continuous functions on \n                  \n                    \n                  \n                  $$\n\\mathbb{T}\n$$\n                , and the function g: \n                  \n                    \n                  \n                  $$\n\\mathbb{T} \\to \\mathbb{T}\n$$\n                 satisfies limt→∞\n                        g(t) = ∞ and f ∈ C\n                        \n                  \n                    \n                  \n                  $$\n\\left( {\\mathbb{T} \\times \\mathbb{R}, \\mathbb{R}} \\right)\n$$\n                . Our results are new for third order delay dynamic equations and extend many known results for oscillation of third order dynamic equations. Some examples are given to illustrate the main results.",{"EN":420},"Oscillation of third order nonlinear functional dynamic equations on time scales",{"VOID":422},"10.1007\u002Fs12591-010-0005-y","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs12591-010-0005-y",[425,440,452],{"id":426,"sortIndex":110,"researcher":20,"roles":427,"affiliations":428,"properties":437},"ece2d3d1-3328-4418-adef-a0ce534ffd5f",[142],[429],{"id":20,"sortIndex":21,"affiliation":430,"properties":20},{"id":431,"createTime":432,"updateTime":432,"relativeEntities":433,"slug":20,"properties":434,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"6434ca20-2bab-43cb-9dc1-49c0540cb56f","2023-12-25T18:41:50.543+00:00",[],{"title":435},{"VI":436},"Department of Mathematics, University of Nebraska-Lincoln, Lincoln, USA",{"title":438},{"VI":439},"Allan Peterson",{"id":441,"sortIndex":21,"researcher":20,"roles":442,"affiliations":443,"properties":449},"14dc991c-0cfe-4cc4-8fe6-5a024bd13589",[142],[444],{"id":20,"sortIndex":21,"affiliation":445,"properties":20},{"id":431,"createTime":432,"updateTime":432,"relativeEntities":446,"slug":20,"properties":447,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":448},{"VI":436},{"title":450},{"VI":451},"Lynn Erbe",{"id":453,"sortIndex":109,"researcher":20,"roles":454,"affiliations":455,"properties":464},"512a6e6f-5db1-4e55-83be-7b8ec5fd21f0",[142],[456],{"id":20,"sortIndex":21,"affiliation":457,"properties":20},{"id":458,"createTime":459,"updateTime":459,"relativeEntities":460,"slug":20,"properties":461,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"cae36480-cb91-4d75-a8c7-fab73c8a5c62","2024-01-12T09:41:34.848+00:00",[],{"title":462},{"VI":463},"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt",{"title":465},{"VI":466},"Taher S. Hassan",{"url":423,"publisher":468,"properties":496},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":469,"slug":10,"properties":470,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":474,"manageAffiliations":475,"indexDatabases":476,"url":104,"thumbnailPath":20,"statistic":491,"gsStatistic":20,"type":113,"analyzePriority":20},[],{"issn":471,"eissn":472,"title":473},{"VOID":13},{"VOID":15},{"EN":17},[],[],[477,484],{"id":66,"indexDatabase":478,"url":79,"indexYears":80,"academicFieldIds":483,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":479,"label":480,"description":481,"key":76,"publicationTags":482,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"id":86,"indexDatabase":485,"url":101,"indexYears":20,"academicFieldIds":490,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":486,"label":487,"description":488,"key":97,"publicationTags":489,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"impactFactor":21,"impactFactorByYear":492,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":107,"totalPublicationByYear":493,"totalCitation":21,"totalCitationByYear":494,"totalCitationPerPublication":21,"totalCitationPerPublicationByYear":495,"hindexLast5Year":21,"hindex":21},{},{"2015":109,"2016":110,"2018":109,"2019":110,"2021":110,"2024":109},{},{},{"volume":497,"pages":499},{"VOID":498},"18",{"VOID":500},"199-227","2010-04-27",2010,{"id":504,"createTime":505,"updateTime":506,"relativeEntities":507,"slug":508,"properties":509,"entityType":133,"verifyStatus":134,"verifyTime":506,"verifyNote":136,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":518,"fullTextUrl":20,"authors":519,"publicationType":193,"publisherRelationship":552,"citationCount":20,"citationInfo":20,"publishDate":586,"publishYear":587,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":407},"c1793579-6934-47f9-93bf-0ba2e30fa532","2024-01-04T15:38:20.452+00:00","2025-01-01T23:56:28.176+00:00",[],"Linearized-Stability-for-a-New-Class-of-Neutral-Equations-with-State-Dependent-Delay",{"references":510,"abstract":512,"title":514,"doi":516},{"VOID":511},"Barbarossa, M.V.: On a class of neutral equations with state-dependent delay in population dynamics. Doctoral Dissertation, Technical University Munich, Munich (2013)\nBarbarossa, M.V., Hadeler, K.P., Kuttler, C.: State-dependent neutral delay equations from population dynamics, submitted for publication (2013)\nHale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)\nHale, J.K., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer, New York (1993)\nKuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, Boston (1993)\nMallet-Paret, J., Nussbaum, R.D., Paraskevopoulos, P.: Periodic solutions for functional differential equations with multiple state-dependent time lags. Topol. Methods Nonlinear Anal. 3(1), 101–162 (1994)\nWalther, H.-O.: Smoothness properties of semiflows for differential equations with state dependent delay. In: Proceedings of the International Conference on Differential and Functional Differential Equations (Russian), Moscow, 2002. Moscow State Aviation Institute (MAI), Moscow (2003). English version. In: Journal of the Mathematical Sciences, 12, pp. 5193–5207 (2004)\nWalther, H.-O.: Linearized stability for semiflows generated by a class of neutral equations, with applications to state-dependent delays. J. Dyn. Differ. Equ. 22(3), 439–462 (2010)\nWalther, H.-O.: More on linearized stability for neutral equations with state-dependent delay. Differ. Equ. Dyn. Syst. 19, 315–333 (2011)\nWalther, H.-O.: Semiflows for neutral equations with state-dependent delays. Infinite Dymensional Dynamical Systems. In: Mallet-Paret, J., Wu, J., Yi, Y., Zhu, H. (eds.) Fields Institute Communications, vol. 64, pp. 211–267. Springer, New York (2013)",{"EN":513},"For neutral delay differential equations of the form \n                  \n                    \n                  \n                  $$\\begin{aligned} \\dot{x}(t)=g(\\partial x_t,x_t), \\end{aligned}$$\n                  \n                    \n                  \n                with \n                  \n                    \n                  \n                  $$g$$\n                  \n                    \n                  \n                 defined on an open subset of the space \n                  \n                    \n                  \n                  $$C([-h,0],\\mathbb {R}^n)\\times C^1([-h,0],\\mathbb {R}^n)$$\n                  \n                    \n                  \n                , we extend an earlier principle of linearized stability. The present result applies to a wider class of neutral differential equations \n                  \n                    \n                  \n                  $$\\begin{aligned} \\dot{x}(t) = f(x(t),\\dot{x}(t-\\tau (x(t))), x(t-\\sigma (x(t)))) \\end{aligned}$$\n                  \n                    \n                  \n                with state-dependent delays which includes models for population dynamics with maturation delay.",{"EN":515},"Linearized Stability for a New Class of Neutral Equations with State-Dependent Delay",{"VOID":517},"10.1007\u002Fs12591-014-0204-z","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs12591-014-0204-z",[520,535],{"id":521,"sortIndex":109,"researcher":20,"roles":522,"affiliations":523,"properties":532},"752cdab4-5abe-44c1-b853-a47881d95c63",[142],[524],{"id":20,"sortIndex":21,"affiliation":525,"properties":20},{"id":526,"createTime":527,"updateTime":527,"relativeEntities":528,"slug":20,"properties":529,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"17ad574b-1767-4631-b428-3e9b1be2fb1d","2024-01-04T15:38:20.484+00:00",[],{"title":530},{"VI":531},"Mathematisches Institut, Universität Gießen, Giessen, Germany",{"title":533},{"VI":534},"H. -O. Walther",{"id":536,"sortIndex":21,"researcher":20,"roles":537,"affiliations":538,"properties":549},"1c3ce9d8-d670-4e2a-a88d-42fa17aac2d0",[142],[539],{"id":20,"sortIndex":21,"affiliation":540,"properties":20},{"id":541,"createTime":542,"updateTime":543,"relativeEntities":544,"slug":545,"properties":546,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"5452b603-f5df-4d85-83ef-fe55e0600641","2023-12-11T22:23:58.530+00:00","2024-12-11T00:46:34.239+00:00",[],"Bolyai-Institute-University-of-Szeged-Szeged-Hungary",{"title":547},{"VI":548},"Bolyai Institute, University of Szeged, Szeged, Hungary",{"title":550},{"VI":551},"M. V. Barbarossa",{"url":518,"publisher":553,"properties":581},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":554,"slug":10,"properties":555,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":559,"manageAffiliations":560,"indexDatabases":561,"url":104,"thumbnailPath":20,"statistic":576,"gsStatistic":20,"type":113,"analyzePriority":20},[],{"issn":556,"eissn":557,"title":558},{"VOID":13},{"VOID":15},{"EN":17},[],[],[562,569],{"id":66,"indexDatabase":563,"url":79,"indexYears":80,"academicFieldIds":568,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":564,"label":565,"description":566,"key":76,"publicationTags":567,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"id":86,"indexDatabase":570,"url":101,"indexYears":20,"academicFieldIds":575,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":571,"label":572,"description":573,"key":97,"publicationTags":574,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"impactFactor":21,"impactFactorByYear":577,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":107,"totalPublicationByYear":578,"totalCitation":21,"totalCitationByYear":579,"totalCitationPerPublication":21,"totalCitationPerPublicationByYear":580,"hindexLast5Year":21,"hindex":21},{},{"2015":109,"2016":110,"2018":109,"2019":110,"2021":110,"2024":109},{},{},{"volume":582,"pages":584},{"VOID":583},"24",{"VOID":585},"63-79","2014-04-27",2014,{"id":589,"createTime":590,"updateTime":591,"relativeEntities":592,"slug":593,"properties":594,"entityType":133,"verifyStatus":134,"verifyTime":591,"verifyNote":136,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":603,"fullTextUrl":20,"authors":604,"publicationType":193,"publisherRelationship":632,"citationCount":20,"citationInfo":20,"publishDate":664,"publishYear":665,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":407},"d546a19b-557d-4421-98a5-c8cab8d8bbe4","2024-01-13T11:48:00.153+00:00","2025-01-09T23:45:39.439+00:00",[],"Infinitely-Many-Solutions-for-a-Nonlinear-Elliptic-PDE-with-Multiple-Hardy-Sobolev-Critical-Exponents",{"references":595,"abstract":597,"title":599,"doi":601},{"VOID":596},"Amann, H.: Lusternik-Schnirelman theory and non-linear eigenvalue problems. Math. Ann. 199, 55–72 (1972). https:\u002F\u002Fdoi.org\u002F10.1007\u002FBF01419576\nAmbrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349–381 (1973). https:\u002F\u002Fdoi.org\u002F10.1016\u002F0022-1236(73)90051-7\nAzorero, J.G., Alonso, I.P.: Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term. Trans. Am. Math. Soc. 323, 877 (1991). https:\u002F\u002Fdoi.org\u002F10.2307\u002F2001562\nBartsch, T., Willem, M.: On an elliptic equation with concave and convex nonlinearities. Proc. Am. Math. Soc. 123, 3555–3555 (1995). https:\u002F\u002Fdoi.org\u002F10.1090\u002Fs0002-9939-1995-1301008-2\nBrezis, H., Nirenberg, L.: Positive solutions of nonlinear elliptic equations involving critical sobolev exponents. Commun. Pure Appl. Math. 36, 437–477 (1983). https:\u002F\u002Fdoi.org\u002F10.1002\u002Fcpa.3160360405\nCao, D., Peng, S., Yan, S.: Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth. J. Funct. Anal. 262, 2861–2902 (2012). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.jfa.2012.01.006\nCao, D., Yan, S.: Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential. Calc. Var. Partial Differ. Equ. 38, 471–501 (2010). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00526-009-0295-5\nDevillanova, G., Solimini, S.: Concentration estimates and multiple solutions to elliptic problems at critical growth. Adv. Differ. Equations. 7, 1257–1280 (2002)\nLiu, Z., Han, P.: Infinitely many solutions for elliptic systems with critical exponents. J. Math. Anal. Appl. 353, 544–552 (2009). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.jmaa.2008.12.024\nRabinowitz, P.H.: Variational Methods for Nonlinear Eigenvalue Problems, Eig. Non-Linear Probl. (2009) 139-195. https:\u002F\u002Fdoi.org\u002F10.1007\u002F978-3-642-10940-9_4\nTrudinger, N.: Remarks concerning the conformal deformation of riemannian structures on compact manifolds, Ann. Della Sc. Norm. Super. Di Pisa - Cl. Di Sci. 22 (1968) 265-274\nWillem, M.: Minimax Theorems, BirkhÃuser Boston, Boston, MA, 1996, 55-70. https:\u002F\u002Fdoi.org\u002F10.1007\u002F978-1-4612-4146-1\nYan, S., Yang, J.: Infinitely many solutions for an elliptic problem involving critical Sobolev and Hardy-Sobolev exponents. Calc. Var. Partial Differ. Equ. 48, 587–610 (2013). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00526-012-0563-7",{"EN":598},"In this paper, by an approximating argument, we obtain two disjoint and infinite sets of solutions for the following elliptic equation with multiple Hardy–Sobolev critical exponents \n              \n                \n              \n              $$\\begin{aligned} \\left\\{ \\begin{array}{ll} -\\Delta u=\\mu \\vert u \\vert ^{2^{*}-2} u + \\sum _{i=1}^{l} \\frac{ \\vert u \\vert ^{2^{*}(s_{i})-2}u}{ \\vert x \\vert ^{s_{i}}}+ a(x) \\vert u \\vert ^{q-2} u &{} \\; in \\; \\Omega , \\\\ u=0 &{} \\; on \\; \\partial \\Omega , \\end{array}\\right. \\end{aligned}$$\n              \n            where \n              \n                \n              \n              $$\\Omega $$\n              \n             is a smooth bounded domain in \n              \n                \n              \n              $${\\mathbb {R}}^{N}$$\n              \n             with \n              \n                \n              \n              $$0\\in \\partial \\Omega $$\n              \n             and all the principle curvatures of \n              \n                \n              \n              $$ \\partial \\Omega $$\n              \n             at 0 are negative, \n              \n                \n              \n              $$a \\in {\\mathcal {C}}^{1}({\\bar{\\Omega }}, \\mathbb {R^{*}}^{+}),$$\n              \n             \n              \n                \n              \n              $$ \\mu > 0,$$\n              \n             \n              \n                \n              \n              $$0\u003Cs_{1}\u003Cs_{2}\u003C...\u003Cs_{l}\u003C2,$$\n              \n             \n              \n                \n              \n              $$1\u003Cq\u003C2$$\n              \n             and \n              \n                \n              \n              $$N > 2\\frac{q+1}{q -1}.$$\n              \n             By \n              \n                \n              \n              $$2^{*}:=\\frac{2 N}{N-2}$$\n              \n             and \n              \n                \n              \n              $$2^{*}(s_{i}):=\\frac{2 (N-s_{i})}{N-2}$$\n              \n             we denote the critical Sobolev exponent and Hardy–Sobolev exponents, respectively.",{"EN":600},"Infinitely Many Solutions for a Nonlinear Elliptic PDE with Multiple Hardy–Sobolev Critical Exponents",{"VOID":602},"10.1007\u002Fs12591-023-00629-y","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs12591-023-00629-y",[605,620],{"id":606,"sortIndex":109,"researcher":20,"roles":607,"affiliations":608,"properties":617},"c765046e-3807-4f1d-a15f-c224033b5fcb",[142],[609],{"id":20,"sortIndex":21,"affiliation":610,"properties":20},{"id":611,"createTime":612,"updateTime":612,"relativeEntities":613,"slug":20,"properties":614,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"3392dc92-2535-4d25-a3b4-2dd00494695c","2024-01-11T04:37:15.140+00:00",[],{"title":615},{"VI":616},"Department of Mathematics, Faculty of Sciences, IBN Tofail University, Kenitra, Morocco",{"title":618},{"VI":619},"Rachid 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Math. Anal. Appl.; citation_title=Existence and continuity of global attractors and nonhomogeneous equilibria for a class of evolution equations with nonlocal terms,; citation_author=FDM Bezerra, AL Pereira, SH Silva; citation_volume=396; citation_publication_date=2012; citation_pages=590-600; citation_doi=10.1016\u002Fj.jmaa.2012.06.042; citation_id=CR1\ncitation_journal_title=Nonlinear Anal.; citation_title=A non-autonomous strongly damped wave equation: existence and continuity of the pullback attractor.; citation_author=T Caraballo, AN Carvalho, JA Langa, F Rivero; citation_volume=74; citation_issue=6; citation_publication_date=2011; citation_pages=2272-2283; citation_doi=10.1016\u002Fj.na.2010.11.032; citation_id=CR2\ncitation_journal_title=Internat. J. Bifur. Chaos; citation_title=A gradient-like nonautonomous evolution processes; citation_author=T Caraballo, AN Carvalho, JA Langa, F Rivero; citation_volume=20; citation_issue=9; citation_publication_date=2010; citation_pages=2751-2760; citation_doi=10.1142\u002FS0218127410027337; citation_id=CR3\nCarvalho, A.N., Langa, J.A., Robinson, J.C.: Attractors for infinite-dimensional nonautonomous dynamical systems. Applied Mathematical Sciences, vol. 182. Springer, New York (2012)\nChepyzhov, V.V., Vishik, M.I.: Attractors for equations of mathematical physics. In: Colloquium Publications, vol. 49. America Mathematical Society, Providence, RI (2002)\ncitation_journal_title=Nonlinear Anal.; citation_title=Propagation speed of travelling fronts in nonlocal reaction-diffusion equations; citation_author=J Coville, L Dupaigne; citation_volume=60; citation_publication_date=2005; citation_pages=797-819; citation_doi=10.1016\u002Fj.na.2003.10.030; citation_id=CR6\ncitation_journal_title=Eletron. J. 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Math. Soc.; citation_title=Nonautonomous differential equations and dynamical systems; citation_author=GR Sell; citation_volume=127; citation_publication_date=1967; citation_pages=241-283; citation_id=CR22",{"EN":676},"In this work we consider the nonlocal evolution equation with time-dependent terms which arises in models of phase separation in $$\\mathbb {R}^N$$$$\\begin{aligned} \\partial _t u=- u + g \\left( \\beta (J*u) +\\beta h(t)\\right) \\end{aligned}$$under some restrictions on h, growth restrictions on the nonlinear term g and $$\\beta >1$$. We prove the existence, regularity and upper-semicontinuity of pullback attractors with respect to functional parameter h(t) in some weighted spaces.",{"EN":678},"Pullback Attractors for a Nonlocal Nonautonomous Evolution Model in $$\\mathbb {R}^N$$",{"VOID":680},"10.1007\u002Fs12591-016-0302-1","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs12591-016-0302-1","https:\u002F\u002Flink.springer.com\u002Fcontent\u002Fpdf\u002F10.1007\u002Fs12591-016-0302-1.pdf",[684,700,715],{"id":685,"sortIndex":110,"researcher":20,"roles":686,"affiliations":687,"properties":697},"d396b3c6-4489-454f-8386-e9e5a303d812",[142],[688],{"id":20,"sortIndex":21,"affiliation":689,"properties":20},{"id":690,"createTime":691,"updateTime":691,"relativeEntities":692,"slug":693,"properties":694,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"1ec5378f-28cc-42e0-877d-048020b43f5e","2023-11-26T01:23:44.844+00:00",[],"Unidade-Acad%C3%AAmica-de-Matem%C3%A1tica-Universidade-Federal-de-Campina-Grande-Campina-Grande-Brazil",{"title":695},{"VI":696},"Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, Campina Grande, Brazil",{"title":698},{"VI":699},"da Silva, Severino H.",{"id":701,"sortIndex":21,"researcher":20,"roles":702,"affiliations":703,"properties":712},"f0150fd3-3b16-4897-a512-9320d22531e4",[142],[704],{"id":20,"sortIndex":21,"affiliation":705,"properties":20},{"id":706,"createTime":707,"updateTime":707,"relativeEntities":708,"slug":20,"properties":709,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"0db28e52-2089-41a5-8a17-74d8c97615ff","2024-01-30T07:13:28.167+00:00",[],{"title":710},{"VI":711},"Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, Brazil",{"title":713},{"VI":714},"Bezerra, Flank D. M.",{"id":716,"sortIndex":109,"researcher":20,"roles":717,"affiliations":718,"properties":724},"7367f934-0261-44f0-9971-905c9ec0915c",[142],[719],{"id":20,"sortIndex":21,"affiliation":720,"properties":20},{"id":706,"createTime":707,"updateTime":707,"relativeEntities":721,"slug":20,"properties":722,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":723},{"VI":711},{"title":725},{"VI":726},"Pereira, Miriam da S.",{"url":681,"publisher":728,"properties":756},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":729,"slug":10,"properties":730,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":734,"manageAffiliations":735,"indexDatabases":736,"url":104,"thumbnailPath":20,"statistic":751,"gsStatistic":20,"type":113,"analyzePriority":20},[],{"issn":731,"eissn":732,"title":733},{"VOID":13},{"VOID":15},{"EN":17},[],[],[737,744],{"id":66,"indexDatabase":738,"url":79,"indexYears":80,"academicFieldIds":743,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":739,"label":740,"description":741,"key":76,"publicationTags":742,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"id":86,"indexDatabase":745,"url":101,"indexYears":20,"academicFieldIds":750,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":746,"label":747,"description":748,"key":97,"publicationTags":749,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"impactFactor":21,"impactFactorByYear":752,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":107,"totalPublicationByYear":753,"totalCitation":21,"totalCitationByYear":754,"totalCitationPerPublication":21,"totalCitationPerPublicationByYear":755,"hindexLast5Year":21,"hindex":21},{},{"2015":109,"2016":110,"2018":109,"2019":110,"2021":110,"2024":109},{},{},{"volume":757,"pages":759,"issue":761},{"VOID":758},"28",{"VOID":760},"87-105",{"VOID":762},"1","2020-01-01",2020,{"id":766,"createTime":767,"updateTime":768,"relativeEntities":769,"slug":770,"properties":771,"entityType":133,"verifyStatus":134,"verifyTime":768,"verifyNote":136,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":780,"fullTextUrl":20,"authors":781,"publicationType":193,"publisherRelationship":821,"citationCount":20,"citationInfo":20,"publishDate":855,"publishYear":856,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":407},"0b4de392-4985-4b9b-81cf-8b9fc3757d79","2024-01-14T09:20:00.449+00:00","2024-09-19T23:34:43.516+00:00",[],"Exact-Solutions-of-the-Modified-Benjamin-Bona-Mahoney-mBBM-Equation-by-Using-the-First-Integral-Method",{"references":772,"abstract":774,"title":776,"doi":778},{"VOID":773},"Feng Z.S.: The first integer method to study the Burgers–Korteweg–de Vries equation. J. Phys. A 35(2), 343–349 (2002)\nTaghizadeh N., Mirzazadeh M., Farahrooz F.: Exact solutions of the nonlinear Schröinger equation by the first integral method. J. Math. Anal. Appl. 374, 549–553 (2011)\nRaslan K.R.: The first integral method for solving some important nonlinear partial differential equations. Nonlinear Dyn. 53, 281–286 (2008)\nHosseini K., Ansari R.: Exact solutions of some nonlinear systems of partial differential equations by using the first integral method. J. Math. Anal. Appl. 387, 807–814 (2012)\nTaghizadeh N., Mirzazadeh M.: Filiz Tascan: the first-integral method applied to the Eckhaus equation. Appl. Math. Lett. 25, 798–802 (2012)\nWazwaz A.M., Helal M.A.: Nonlinear variants of the BBM equation with compact and noncompact physical structures. Chaos Soliton Fract. 26, 767–776 (2005)\nNickel J.: Elliptic solutions to a generalized BBM equation. Phys. Lett. A 364, 221–226 (2007)\nWang J.M., Zhang M., Zhang W.L., Zhang R., Hua J.: A new method for constructing travelling wave solutions to the modified Benjamin–Bona–Mahoney equation. Chin. Phys. Lett. 25(7), 2339–2341 (2008)\nLayeni O.P., Akinola A.P.: A new hyperbolic auxiliary function method and exact solutions of the mBBM equation. Commun. Nonlinear Sci. Numer. Simul. 15, 133–138 (2010)\nYan F., Liu H., Liu Z.: The bifurcation and exact travelling wave solutions for the modified Benjamin–Bona–Mahoney (mBBM) equation. Commun. Nonlinear Sci. Numer. Simul. 17, 2824–2832 (2012)",{"EN":775},"In this paper, the first integral method is used to construct exact solutions of the modified Benjamin–Bona–Mahoney (mBBM) equation. This method can be applied to non-integrable equations as well as to integrable ones. By means of this method, some exact solutions of mBBM equations are formally obtained. Obtained results clearly indicate the reliability and efficiency of the first integral method.",{"EN":777},"Exact Solutions of the Modified Benjamin–Bona–Mahoney (mBBM) Equation by Using the First Integral Method",{"VOID":779},"10.1007\u002Fs12591-012-0145-3","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs12591-012-0145-3",[782,797,809],{"id":783,"sortIndex":21,"researcher":20,"roles":784,"affiliations":785,"properties":794},"4b8f7f16-d690-4947-9e7b-c2166afa169b",[142],[786],{"id":20,"sortIndex":21,"affiliation":787,"properties":20},{"id":788,"createTime":789,"updateTime":789,"relativeEntities":790,"slug":20,"properties":791,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"4fd3a9ed-d8d4-4a5c-b076-566743f15e9a","2024-01-14T09:20:00.631+00:00",[],{"title":792},{"VI":793},"Department of Mathematics, Honghe University, Mengzi, People’s Republic of China",{"title":795},{"VI":796},"Yinghui He",{"id":798,"sortIndex":109,"researcher":20,"roles":799,"affiliations":800,"properties":806},"79f88970-6445-4aa0-a9f2-84a20730741e",[142],[801],{"id":20,"sortIndex":21,"affiliation":802,"properties":20},{"id":788,"createTime":789,"updateTime":789,"relativeEntities":803,"slug":20,"properties":804,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":805},{"VI":793},{"title":807},{"VI":808},"Shaolin Li",{"id":810,"sortIndex":110,"researcher":20,"roles":811,"affiliations":812,"properties":818},"80e4280c-3d79-4f6a-8c2e-13bc81f87f6a",[142],[813],{"id":20,"sortIndex":21,"affiliation":814,"properties":20},{"id":788,"createTime":789,"updateTime":789,"relativeEntities":815,"slug":20,"properties":816,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":817},{"VI":793},{"title":819},{"VI":820},"Yao Long",{"url":780,"publisher":822,"properties":850},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":823,"slug":10,"properties":824,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":828,"manageAffiliations":829,"indexDatabases":830,"url":104,"thumbnailPath":20,"statistic":845,"gsStatistic":20,"type":113,"analyzePriority":20},[],{"issn":825,"eissn":826,"title":827},{"VOID":13},{"VOID":15},{"EN":17},[],[],[831,838],{"id":66,"indexDatabase":832,"url":79,"indexYears":80,"academicFieldIds":837,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":833,"label":834,"description":835,"key":76,"publicationTags":836,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"id":86,"indexDatabase":839,"url":101,"indexYears":20,"academicFieldIds":844,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":840,"label":841,"description":842,"key":97,"publicationTags":843,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"impactFactor":21,"impactFactorByYear":846,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":107,"totalPublicationByYear":847,"totalCitation":21,"totalCitationByYear":848,"totalCitationPerPublication":21,"totalCitationPerPublicationByYear":849,"hindexLast5Year":21,"hindex":21},{},{"2015":109,"2016":110,"2018":109,"2019":110,"2021":110,"2024":109},{},{},{"volume":851,"pages":853},{"VOID":852},"21",{"VOID":854},"199-204","2012-09-06",2012,{"id":858,"createTime":859,"updateTime":860,"relativeEntities":861,"slug":862,"properties":863,"entityType":133,"verifyStatus":134,"verifyTime":860,"verifyNote":136,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":872,"fullTextUrl":20,"authors":873,"publicationType":193,"publisherRelationship":901,"citationCount":20,"citationInfo":20,"publishDate":934,"publishYear":502,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":407},"9784f416-f336-4710-8b35-81432b2e40ab","2023-12-12T17:09:39.307+00:00","2024-12-18T23:28:24.642+00:00",[],"Whether-chaos-can-be-achieved-in-piecewise-linear-boundary-value-problems",{"references":864,"abstract":866,"title":868,"doi":870},{"VOID":865},"Sharkovsky A. N., Difference equations and boundary value problems, in: New Progress in Difference Equations, Proc. ICDEA’2001, Taylor & Francis, London, 3–22, (2004)\nSharkovsky A. N., Maistrenko Yu. L. and Romanenko E. Yu., Difference equations and their applications, Ser. Math. and its Appl., Dordrecht: Kluwer Acad. Publ., 250, (1993)\nRomanenko E. Yu. and Sharkovsky A. N., From boundary value problems to difference equations: A method of investigation of chaotic vibrations, Intern. J. Bifurcation and Chaos, 9(7), 1285–1306, (1999)\nSharkovsky A. N. and Romanenko E. Yu., Difference equations and dynamical systems generated by certain classes of boundary value problems, Proceedings of Steklov Institute of Mathematics, Moscow, 244, 264–279, (2004)\nSharkovsky A. N. and Romanenko E. Yu., Turbulence: Ideal, Encyclopedia of Nonlinear Science (ed. Alwyn Scott), New York and London: Routledge, 955–957, (2005)\nSharkovsky A. N., Ideal turbulence, Nonlinear Dynamics, 44, 15–27, (2006)\nRomanenko E. Yu. and Sharkovsky A. N., Dynamics of solutions for simplest nonlinear boundary value problems, Ukrain. Math. J., 51(6), 820–826, (1999)\nRomanenko E. Yu., Randomness in deterministic difference equations, J. Difference Equations and Appl., 16(2–3), 243–268, (2010)",{"EN":867},"We show that chaos in piecewise linear partial differential equations with linear boundary conditions is realizable: even the simplest boundary value problems of this kind can possess chaotic solutions in an open region of the parameter space.",{"EN":869},"Whether chaos can be achieved in piecewise linear boundary value problems",{"VOID":871},"10.1007\u002Fs12591-010-0007-9","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs12591-010-0007-9",[874,889],{"id":875,"sortIndex":109,"researcher":20,"roles":876,"affiliations":877,"properties":886},"4acb1992-ba59-4419-9570-3f1296204385",[142],[878],{"id":20,"sortIndex":21,"affiliation":879,"properties":20},{"id":880,"createTime":881,"updateTime":881,"relativeEntities":882,"slug":20,"properties":883,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"5125ac5c-c8c6-44dc-9de8-859cf2cad8ce","2023-12-12T17:09:25.462+00:00",[],{"title":884},{"VI":885},"Institute of Mathematics, National Academy of Science of Ukraine, Kiev, Ukraine",{"title":887},{"VI":888},"A. N. Sharkovsky",{"id":890,"sortIndex":21,"researcher":20,"roles":891,"affiliations":892,"properties":898},"dc1c0028-6914-4e8d-b340-5da870174d0d",[142],[893],{"id":20,"sortIndex":21,"affiliation":894,"properties":20},{"id":880,"createTime":881,"updateTime":881,"relativeEntities":895,"slug":20,"properties":896,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":897},{"VI":885},{"title":899},{"VI":900},"E. Yu. Romanenko",{"url":872,"publisher":902,"properties":930},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":903,"slug":10,"properties":904,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":908,"manageAffiliations":909,"indexDatabases":910,"url":104,"thumbnailPath":20,"statistic":925,"gsStatistic":20,"type":113,"analyzePriority":20},[],{"issn":905,"eissn":906,"title":907},{"VOID":13},{"VOID":15},{"EN":17},[],[],[911,918],{"id":66,"indexDatabase":912,"url":79,"indexYears":80,"academicFieldIds":917,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":913,"label":914,"description":915,"key":76,"publicationTags":916,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"id":86,"indexDatabase":919,"url":101,"indexYears":20,"academicFieldIds":924,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":920,"label":921,"description":922,"key":97,"publicationTags":923,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"impactFactor":21,"impactFactorByYear":926,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":107,"totalPublicationByYear":927,"totalCitation":21,"totalCitationByYear":928,"totalCitationPerPublication":21,"totalCitationPerPublicationByYear":929,"hindexLast5Year":21,"hindex":21},{},{"2015":109,"2016":110,"2018":109,"2019":110,"2021":110,"2024":109},{},{},{"volume":931,"pages":932},{"VOID":498},{"VOID":933},"1-9","2010-05-27",{"id":936,"createTime":937,"updateTime":937,"relativeEntities":938,"slug":20,"properties":939,"entityType":133,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":948,"fullTextUrl":20,"authors":949,"publicationType":193,"publisherRelationship":981,"citationCount":20,"citationInfo":20,"publishDate":1015,"publishYear":1016,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":407},"0a89639e-d5fb-417b-b62d-189eecfad482","2023-12-17T23:23:10.538+00:00",[],{"references":940,"abstract":942,"title":944,"doi":946},{"VOID":941},"Ezzinbi, K., Toure, H., Zabsonre, I.: Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces. Nonlinear Anal. 70, 2761–2771 (2009)\nBalachandran, K., Sakthivel, R.: Controllability of functional semilinear integrodifferential systems in Banch spaces. J. Math. Anal. Appl. 255, 447–457 (2001)\nBalachandran, K., Park, J.Y.: Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces. Math. Probl. Eng. 2003(2), 65–79 (2003)\nChang, Y.K., Nieto, J.J., Li, W.S.: Controllability of semilinear differential systems with nonlocal initial conditions in Banach spaces. J. Optim. Theory Appl. 142, 267–273 (2009)\nWang, J.R., Fan, Z., Zhou, Y.: Nonlocal controllability of semilinear dynamic systems with fractional derivative in Banach spaces. J. Optim. Theory Appl. 154, 292–302 (2012)\nEzzinbi, K., Degla, G., Ndambomve, P.: Controllability for some partial functional integrodifferential equations with nonlocal condition in Banach spaces. Discussiones Mathematicae Differ. Incl. Control Optim. 35(1), 1–22 (2015)\nMachado, J.A., Ravichandran, C., Rivero, M., Trujillo, J.J.: Controllability results for impulsive mixed-type functional integro-differential evolution equations with nonlocal conditions. Fixed Point Theory Appl. 2013, 66 (2013)\nLi, M., Wang, M., Zhang, F.: Controllability of impulsive functional differential systems in Banach spaces. Chaos Solitons Fractals 29, 175–181 (2006)\nAtmania, R., Mazouzi, S.: Controllability of semilinear integrodifferential equations with nonlocal conditions. Electron. J. Differ. Equ. 2005(75), 1–9 (2005)\nSakthivel, R., Mahmudov, N.I., Nieto, J.J.: Controllability for a class of fractional-order neutral evolution control systems. Appl. Math. Comput. 218, 10334–10340 (2012)\nBaghli, S., Benchohra, M., Ezzinbi, K.: Controllability results for semilinear functional and neutral functional evolution equations with infinite delay. Surv. Math. Appl. 4, 15–39 (2009)\nSelvi, S., Arjunan, M.M.: Controllability results for impulsive differential systems with finite delay. J. Nonlinear Sci. Appl. 5, 206–219 (2012)\nLorenzi, A., Sinestrari, E.: An inverse problem in the theory of materials with memory. Nonlinear Anal. Theory Methods Appl. 12(12), 1317–1335 (1988)\nGrimmer, R.: Resolvent operators for integral equations in a Banach space. Trans. Am. Math. Soc. 273, 333–349 (1983)\nDesch, W., Grimmer, R., Schappacher, W.: Some considerations for linear integrodifferential equations. J. Math. Anal. Appl. 104, 219–234 (1984)\nDafermos, C.M., Nohelj, A.: Energy methods for non linear hyperbolic Volterra integrodifferential equations. Commun. Partial Differ. Equ. 4, 219–278 (1979)\nGurtin, M.E., Pipkin, A.C.: A general theory of heat conduction with finite wave speeds. Arch. Ration. Mech. Anal. 31, 113–126 (1968)\nSinestrari, E.: An integrodifferential equation arising from the theory of nonlinear heat flow with memory. In: Boccardo, L., Tesei, A. (eds.) Nonlinear Parabolic Equations: Qualitative Properties of Solutions. Research Notes in Mathematics, vol. 149, pp. 207–218. Longman, Harlow (1987)\nGrimmer, R., Pritchard, A.J.: Analytic resolvent operators for integral equations in Banach space. J. Differ. Equ. 50, 234–259 (1983)\nGrimmer, R., Kappelf, C.: Series expansions for resolvents of Volterra integrodifferential equations in Banach space. SIAM J. Math. Anal. 15, 595–604 (1984)\nLunardi, A., Sinestrari, E.: \\(C^{\\alpha }\\)-regularity for non autonomous linear integrodifferential equations of parabolic type. J. Differ. Equ. 68, 88–116 (1986)\nTravis, C.C., Webb, G.F.: Existence and stability for partial functional differential equations. Trans. Am. Math. Soc. 200, 395–418 (1974)\nLiang, J., Liu, J.H., Xiao, T.-J.: Nonlocal problems for integrodifferential equations. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 15, 815–824 (2008)\nBanas, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Lecture Notes in Pure and Applied Mathematics, vol. 60. Marcel Dekker, New York (1980)\nMönch, H.: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlinear Anal. Theory Methods Appl. 4(5), 985–999 (1980)\nQuinn, M.D., Carmichael, N.: An approach to nonlinear control problem using fixed point methods, degree theory and pseudo-inverses. Numer. Funct. Anal. Optim. 7, 197–219 (1984)",{"EN":943},"This work concerns the study of the controllability for some nonlinear partial functional integrodifferential equation with finite delay arising in the modelling of materials with memory in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator. An example of applications is given for illustration.",{"EN":945},"On the Controllability of Some Nonlinear Partial Functional Integrodifferential Equations with Finite Delay in Banach Spaces",{"VOID":947},"10.1007\u002Fs12591-017-0386-2","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs12591-017-0386-2",[950,965],{"id":951,"sortIndex":109,"researcher":20,"roles":952,"affiliations":953,"properties":962},"5e058fea-d27e-445f-a68f-dd270f3e9880",[142],[954],{"id":20,"sortIndex":21,"affiliation":955,"properties":20},{"id":956,"createTime":957,"updateTime":957,"relativeEntities":958,"slug":20,"properties":959,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"b5fb0d52-a824-4243-901b-44105cfe7ec4","2024-01-19T11:35:47.667+00:00",[],{"title":960},{"VI":961},"Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, Marrakech, Morocco",{"title":963},{"VI":964},"Khalil Ezzinbi",{"id":966,"sortIndex":21,"researcher":20,"roles":967,"affiliations":968,"properties":978},"09ece8e4-7d11-48b6-a8a6-697f6c4dfde8",[142],[969],{"id":20,"sortIndex":21,"affiliation":970,"properties":20},{"id":971,"createTime":972,"updateTime":972,"relativeEntities":973,"slug":974,"properties":975,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"b91311ca-f4f0-4717-ab8d-900fc96efcf3","2024-04-05T16:50:56.409+00:00",[],"Department-of-Mathematics-Faculty-of-Science-University-of-Buea-Buea-Cameroon",{"title":976},{"VI":977},"Department of Mathematics, Faculty of Science, University of Buea, Buea, Cameroon",{"title":979},{"VI":980},"Patrice Ndambomve",{"url":948,"publisher":982,"properties":1010},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":983,"slug":10,"properties":984,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":988,"manageAffiliations":989,"indexDatabases":990,"url":104,"thumbnailPath":20,"statistic":1005,"gsStatistic":20,"type":113,"analyzePriority":20},[],{"issn":985,"eissn":986,"title":987},{"VOID":13},{"VOID":15},{"EN":17},[],[],[991,998],{"id":66,"indexDatabase":992,"url":79,"indexYears":80,"academicFieldIds":997,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":993,"label":994,"description":995,"key":76,"publicationTags":996,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"id":86,"indexDatabase":999,"url":101,"indexYears":20,"academicFieldIds":1004,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":1000,"label":1001,"description":1002,"key":97,"publicationTags":1003,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"impactFactor":21,"impactFactorByYear":1006,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":107,"totalPublicationByYear":1007,"totalCitation":21,"totalCitationByYear":1008,"totalCitationPerPublication":21,"totalCitationPerPublicationByYear":1009,"hindexLast5Year":21,"hindex":21},{},{"2015":109,"2016":110,"2018":109,"2019":110,"2021":110,"2024":109},{},{},{"volume":1011,"pages":1013},{"VOID":1012},"29",{"VOID":1014},"673-688","2017-08-23",2017,{"id":1018,"createTime":1019,"updateTime":1019,"relativeEntities":1020,"slug":20,"properties":1021,"entityType":133,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":1030,"fullTextUrl":20,"authors":1031,"publicationType":193,"publisherRelationship":1047,"citationCount":20,"citationInfo":20,"publishDate":1081,"publishYear":1082,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":407},"04fac0cf-efd9-43e5-b87c-2960ceaf4d1b","2024-02-13T23:05:23.175+00:00",[],{"references":1022,"abstract":1024,"title":1026,"doi":1028},{"VOID":1023},"Aronson, D.G.: A comparison method for stability analysis of nonlinear parabolic problems. SIAM Rev. 20, 245–264 (1978)\nAsif, N.A., Khan, R.A.: Positive solutions to singular system with four-point coupled boundary conditions. J. Math. Anal. Appl. 386(2), 848–861 (2012)\nBaleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus: Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, vol. 3. World Scientific, Boston (2012)\nDas, S.: Functional fractional calculus for system identification and control. Springer, New York (2008)\nDeng, K.: Blow-up rates for parabolic systems. Z. Angew. Math. Phys. 47(1), 132–143 (1996)\nDeng, K.: Global existence and blow-up for a system of heat equations with non-linear boundary conditions. Math. Methods Appl. Sci. 18(4), 307–315 (1995)\nHenderson, J., Luca, R.: Positive solutions for a system of nonlinear fractional boundary value problems. Fract. Calc. Appl. Anal. 16(4), 985–1008 (2013)\nHenderson, J., Luca, R.: Nonexistence of positive solutions for a system of coupled fractional boundary value problems. Bound. Value Prob. 2015, 138 (2015). https:\u002F\u002Fdoi.org\u002F10.1186\u002Fs13661-015-0403-8\nHenderson, J., Luca, R.: Positive solutions for a system of semipositone coupled fractional boundary value problems. Bound. Value Prob. 2016, 61 (2016). https:\u002F\u002Fdoi.org\u002F10.1186\u002Fs13661-016-0569-8\nHenderson, J., Luca, R.: Positive solutions for a system of fractional differential equations with coupled integral boundary conditions. Appl. Math. Comput. 249, 182–197 (2014)\nHenderson, J., Luca, R., Tudorache, A.: On a system of fractional differential equations with coupled integral boundary conditions. Fract. Calc. Appl. Anal. 18(2), 361–386 (2015)\nKilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and applications of fractional differential equations. Elsevier, Amsterdam (2006)\nLuka, R., Deliu, C.: Nonexistence of positive solutions for a system of higher-order multi-point boundary value problems. Romai J. 9, 69–77 (2013)\nLuca, R., Tudorache, A.: Positive solutions to a system of semipositone fractional boundary value problems. Adv. Differ. Equ. 2014, 179 (2014)\nMiller, K.S., Ross, B.: An introduction to the fractional calculus and fractional differential equations. Wiley, New York (1993)\nPedersen, M., Lin, Z.: Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition. Appl. Math. Lett. 14, 171–176 (2001)\nPodlubny, I.: Fractional differential equations. Academic Press, New York (1999)\nSabatier, J., Agrawal, O.P., Machado, J.A.T. (eds.): Advances in fractional calculus: theoretical developments and applications in physics and engineering. Springer, Dordrecht (2007)\nPrasad, K.R., Krushna, B.M.B., Raju, V.V.R.R.B., Narasimhulu, Y.: Existence of positive solutions for systems of fractional order boundary value problems with Riemann–Liouville derivative. Nonlinear Stud. 24(3), 619–629 (2017)\nRao, S.N., Prasad, K.R.: Nonexistence of positive solutions for a system of nonlinear multi-point boundary value problems on time scales. Math. Commun. 20, 69–81 (2015)\nRao, S.N.: Existence and nonexistence of poaitive solutions for a system of even order dynamic equation on time scales. J. Appl. Math. Inform. 33(5–6), 531–543 (2015)\nRao, S.N., Zico, M.M.: Positive solutions for a coupled system of nonlinear semipositone fractional boundary value problems. Int. J. Differ. Equ. 2019, Article ID 2893857 (2019). https:\u002F\u002Fdoi.org\u002F10.1155\u002F2019\u002F2893857\nRao, S.N., Alesemi, M.: On a coupled system of fractional differential equations with nonlocal non-separated boundary conditions. Adv. Differ. Equ. 2019, 97 (2019)\nYuan, C., Jiang, D., O’Regan, D., Agarwal, R.P.: Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions. Electron. J. Qual. Theory Differ. Equ. 13, 1–17 (2012)\nZhigui, L., Chunhong, X.: The blow-up rate for a system of heat equations with nonlinear boundary conditions. Nonlinear Anal. 34(5), 767–778 (1998)",{"EN":1025},"In this paper, we consider the non-separated boundary value problem for system of nonlinear Riemann–Liouville fractional differential equations \n                \n                  \n                \n                $$\\begin{aligned} \\begin{aligned} D_{0^+}^{\\alpha }x(t)+\\lambda f(t, x(t), y(t))=0,~~0\u003Ct\u003C1,\\\\ D_{0^+}^{\\alpha }y(t)+\\mu g(t, x(t), y(t))=0, ~~0\u003Ct\u003C1, \\end{aligned} \\end{aligned}$$\n                \n              subject to the boundary conditions \n                \n                  \n                \n                $$\\begin{aligned} \\begin{aligned} x(0)=y(0)=0,~~ u_1D_{0^+}^{\\beta }x(1)=v_1D_{0^+}^{\\beta }y(\\xi ),\\\\ u_2D_{0^+}^{\\beta }y(1)=v_2D_{0^+}^{\\beta }x(\\eta ),~~\\eta ,\\xi \\in (0,1), \\end{aligned} \\end{aligned}$$\n                \n              where the coefficients \n                \n                  \n                \n                $$u_{i},v_{i},i=1,2$$\n                \n               are real positive constants, we give sufficient conditions on \n                \n                  \n                \n                $$\\lambda , \\mu , f$$\n                \n               and g such that the system has no positive solutions. An example is given to demonstrate the main result.",{"EN":1027},"The Nonexistence of Positive Solutions for A Coupled System of Non-separated Boundary Value Problems",{"VOID":1029},"10.1007\u002Fs12591-019-00510-x","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs12591-019-00510-x",[1032],{"id":1033,"sortIndex":21,"researcher":20,"roles":1034,"affiliations":1035,"properties":1044},"b6be6051-e84c-49f8-81e6-04ca62d908d0",[142],[1036],{"id":20,"sortIndex":21,"affiliation":1037,"properties":20},{"id":1038,"createTime":1039,"updateTime":1039,"relativeEntities":1040,"slug":20,"properties":1041,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"f049b834-7f4c-44e2-a695-54d4ac64c8a6","2024-02-13T23:05:23.193+00:00",[],{"title":1042},{"VI":1043},"Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia",{"title":1045},{"VI":1046},"Sabbavarapu Nageswara Rao",{"url":1030,"publisher":1048,"properties":1076},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1049,"slug":10,"properties":1050,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":1054,"manageAffiliations":1055,"indexDatabases":1056,"url":104,"thumbnailPath":20,"statistic":1071,"gsStatistic":20,"type":113,"analyzePriority":20},[],{"issn":1051,"eissn":1052,"title":1053},{"VOID":13},{"VOID":15},{"EN":17},[],[],[1057,1064],{"id":66,"indexDatabase":1058,"url":79,"indexYears":80,"academicFieldIds":1063,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":1059,"label":1060,"description":1061,"key":76,"publicationTags":1062,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"id":86,"indexDatabase":1065,"url":101,"indexYears":20,"academicFieldIds":1070,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":1066,"label":1067,"description":1068,"key":97,"publicationTags":1069,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"impactFactor":21,"impactFactorByYear":1072,"i10Index":21,"i10IndexLast5Year":21,"totalPublication":107,"totalPublicationByYear":1073,"totalCitation":21,"totalCitationByYear":1074,"totalCitationPerPublication":21,"totalCitationPerPublicationByYear":1075,"hindexLast5Year":21,"hindex":21},{},{"2015":109,"2016":110,"2018":109,"2019":110,"2021":110,"2024":109},{},{},{"volume":1077,"pages":1079},{"VOID":1078},"31",{"VOID":1080},"1-15","2019-12-13",2019,{"id":1084,"createTime":1085,"updateTime":1086,"relativeEntities":1087,"slug":1088,"properties":1089,"entityType":133,"verifyStatus":134,"verifyTime":1086,"verifyNote":136,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":1098,"fullTextUrl":20,"authors":1099,"publicationType":193,"publisherRelationship":1127,"citationCount":20,"citationInfo":20,"publishDate":1161,"publishYear":1082,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":407},"183966ba-3df7-49d4-aeaa-8087f4a8102e","2024-01-18T17:22:07.752+00:00","2025-02-15T23:03:11.055+00:00",[],"Convergence-for-Slow-Discrete-Dynamical-Systems-with-Identity-Linearization",{"references":1090,"abstract":1092,"title":1094,"doi":1096},{"VOID":1091},"De La Parra, R.B., Marvá, M., Sánchez, E., Sanz, L.: Reduction of discrete dynamical systems with applications to dynamics population models. Math. Model. Nat. Phenom. 8(6), 107–129 (2013)\nSolis, F.J., Gonzalez, L.M.: Modeling the effects of human papilloma virus in cervical cells. Int. J. Comput. Math. 91, 1–9 (2013). https:\u002F\u002Fdoi.org\u002F10.1080\u002F00207160.2013.770843\nWerbos, P.J.: 3-Brain architecture for an intelligent decision and control system. US Patent No. 6,169,981, 2001\nZhang, L., Mykland, P.A., Aït-Sahalia, Y.: A tale of two time scales. J. Am. Stat. Assoc. 100, 1394–1411 (2012)\nGivon, D., Kupferman, R.: White noise limits for discrete dynamical systems driven by fast deterministic dynamics. Phys. A Stat. Mech. Appl. 335(3–4), 385–412 (2004)\nPavlov, A., van de Wouw, N.: Convergent discrete-time nonlinear systems: the case of PWA systems. In: American Control Conference, IEEE pp. 3452–3457 (2008)\nSanz, L., Bravo de la Parra, R., Sánchez, E.: Approximate reduction of non-linear discrete models with two time scales. J. Differ. Equ. Appl. 14(6), 607–627 (2008)\nSinger, A., Erban, R., Kevrekidis, I.G., Coifman, R.R.: Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps. Proc. Natl. Acad. Sci. 106(38), 16090–16095 (2009)\nSolis, F., Chen, B., Kojouharov, H.: A classification of slow convergence near parametric periodic points of discrete dynamical systems. Int. J. Comput. Math. 93, 1011–1021 (2015). https:\u002F\u002Fdoi.org\u002F10.1080\u002F00207160.2015.1015528\nSolis, F., Chen, B., Kojouharov, H.: Multidimensional Discrete Dynamical Systems with Slow behavior. Differential Equations and Dynamical Systems, pp. 1–12. Springer, New York (2017). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs12591-017-0388-0\nSolis, F., Sotolongo, A.: Convergence on Two Dimensional 1-Slow Discrete Dynamical Systems. Differential Equations and Dynamical Systems, pp. 1–15. Springer, New York (2016). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs12591-016-0330-x\nSolis, F., Sotolongo, A.: On the Unresolved Cases of Convergence of Bidimensional Slow Discrete Dynamical Systems. Differential Equations and Dynamical Systems, pp. 1–23. Springer, New York (2017). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs12591-017-0353-y",{"EN":1093},"In this work we give sufficient and necessary conditions for convergence for nonhyperbolic fixed points of dynamical systems of arbitrary dimension whose linearization around zero is the identity function. To achieve this goal, we first rewrite the dynamical system in terms of spherical polar coordinates and by approximation of the radial iteration function we discover a necessary condition depending on a remarkable angular function. Searching for conditions that are sufficient, we discover more angular functions that together with the first one gives a complete set that plays the role of the iteration derivative for unidimensional discrete systems.",{"EN":1095},"Convergence for Slow Discrete Dynamical Systems with Identity Linearization",{"VOID":1097},"10.1007\u002Fs12591-019-00501-y","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs12591-019-00501-y",[1100,1115],{"id":1101,"sortIndex":21,"researcher":20,"roles":1102,"affiliations":1103,"properties":1112},"6fd71b62-5115-431b-98ad-e4a3aa9b06fb",[142],[1104],{"id":20,"sortIndex":21,"affiliation":1105,"properties":20},{"id":1106,"createTime":1107,"updateTime":1107,"relativeEntities":1108,"slug":20,"properties":1109,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"21a9d00b-eca3-4c70-8c29-98a67493e1e3","2024-01-11T12:09:24.657+00:00",[],{"title":1110},{"VI":1111},"CIMAT, Guanajuato, Mexico",{"title":1113},{"VI":1114},"Alina Sotolongo",{"id":1116,"sortIndex":109,"researcher":20,"roles":1117,"affiliations":1118,"properties":1124},"0fc3ef97-477c-4038-a4c1-5453174bf23f",[142],[1119],{"id":20,"sortIndex":21,"affiliation":1120,"properties":20},{"id":1106,"createTime":1107,"updateTime":1107,"relativeEntities":1121,"slug":20,"properties":1122,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":1123},{"VI":1111},{"title":1125},{"VI":1126},"Francisco J. 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