Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators

Chaos - Tập 27 Số 7 - 2017
Lia Papadopoulos1, Jason Z. Kim2, Jürgen Kurths3,4,5, Danielle S. Bassett2,6
1Department of Physics and Astronomy, University of Pennsylvania 1 , Philadelphia, Pennsylvania 19104, USA
2Department of Bioengineering, University of Pennsylvania 2 , Philadelphia, Pennsylvania 19104, USA
3Department of Physics, Humboldt University of Berlin 4 , 12489 Berlin, Germany
4Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen 5 AB24 3UE, United Kingdom
5Potsdam Institute for Climate Impact Research - Telegraphenberg A 31 3 , 14473 Potsdam, Germany
6Department of Electrical and Systems Engineering, University of Pennsylvania 6 , Philadelphia, Pennsylvania 19104, USA

Tóm tắt

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior, and it is interesting to ask how the structural organization of network interactions influences this process. Several studies have explored and uncovered optimal topologies for synchronization by making purposeful alterations to a network. On the other hand, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. However, this co-evolution and the extent to which the dynamics of the individual units can shape the organization of the network itself are less well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. In particular, the system employs a co-evolutionary rewiring strategy that depends only on the instantaneous, pairwise phase differences of neighboring oscillators, and that conserves the total number of edges, allowing the effects of local reorganization to be isolated. We find that a simple rule—which preserves connections between more out-of-phase oscillators while rewiring connections between more in-phase oscillators—can cause initially disordered networks to organize into more structured topologies that support enhanced synchronization dynamics. We examine how this process unfolds over time, finding a dependence on the intrinsic frequencies of the oscillators, the global coupling, and the network density, in terms of how the adaptive mechanism reorganizes the network and influences the dynamics. Importantly, for large enough coupling and after sufficient adaptation, the resulting networks exhibit interesting characteristics, including degree–frequency and frequency–neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions in which the networks were constructed using global information. On the contrary, by considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena and organization can arise in complex systems utilizing local rules.

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Tài liệu tham khảo

2003, SIAM Rev., 45, 167, 10.1137/S003614450342480

2006, Phys. Rep., 424, 175, 10.1016/j.physrep.2005.10.009

2008, Dynamical Processes on Complex Networks

2012, Nat. Phys., 8, 32, 10.1038/nphys2160

2010, Mathematical Foundations of Neuroscience

1999, Neural Comput., 11, 1621, 10.1162/089976699300016179

2000, J. Comput. Neurosci., 8, 183, 10.1023/A:1008925309027

2000, Phys. Rev. E, 62, 5565, 10.1103/PhysRevE.62.5565

2000, Phys. Rev. Lett., 84, 2758, 10.1103/PhysRevLett.84.2758

2004, Phys. Rev. Lett., 92, 074103, 10.1103/PhysRevLett.92.074103

2004, Phys. Rev. Lett., 92, 198101, 10.1103/PhysRevLett.92.198101

2012, Phys. Rev. E, 86, 036105, 10.1103/PhysRevE.86.036105

2014, Math. Modell. Nat. Phenom., 9, 4, 10.1051/mmnp/20149202

2015, Rev. Mod. Phys., 87, 925, 10.1103/RevModPhys.87.925

2002, Eur. Phys. J. B - Condens. Matter Complex Syst., 26, 521, 10.1140/epjb/e20020122

2004, Nat. Rev. Genet., 5, 101, 10.1038/nrg1272

2008, Nat. Rev. Mol. Cell Biol., 9, 770, 10.1038/nrm2503

2000, Nature, 403, 335, 10.1038/35002125

2004, Nature, 431, 308, 10.1038/nature02782

1980, The Geometry of Biological Time

2003, Sync: The Emerging Science of Spontaneous Order

2003, Synchronization: A Universal Concept in Nonlinear Sciences

2004, Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems

2008, Phys. Rep., 469, 93, 10.1016/j.physrep.2008.09.002

2001, Nature, 410, 277, 10.1038/35065745

2005, Trends Cognit. Sci., 9, 474, 10.1016/j.tics.2005.08.011

2006, Proc. Natl. Acad. Sci. U.S.A., 103, 19518, 10.1073/pnas.0606005103

2015, PLOS Comput. Biol., 11, e1004608, 10.1371/journal.pcbi.1004608

2011, Nat. Rev. Neurosci., 12, 43, 10.1038/nrn2961

2009, Proc. Natl. Acad. Sci. U.S.A., 106, 11747, 10.1073/pnas.0903641106

2000, Neural Networks, 13, 909, 10.1016/S0893-6080(00)00053-8

2004, Neurosci. Lett., 355, 25, 10.1016/j.neulet.2003.10.063

2000, Proc. Natl. Acad. Sci. U.S.A., 97, 1867, 10.1073/pnas.97.4.1867

2001, Nat. Rev. Neurosci., 2, 704, 10.1038/35094565

2005, Proc. Natl. Acad. Sci. U.S.A., 102, 9673, 10.1073/pnas.0504136102

2004, Science, 304, 1926, 10.1126/science.1099745

2001, Nat. Rev. Neurosci., 2, 229, 10.1038/35067550

2012, Eur. Phys. J. B, 85, 231, 10.1140/epjb/e2012-30209-9

2012, SIAM J. Control Optim., 50, 1616, 10.1137/110851584

2012, Phys. Rev. Lett., 109, 064101, 10.1103/PhysRevLett.109.064101

2013, Nat. Phys., 9, 191, 10.1038/nphys2535

Araki, 1975, International Symposium on Mathematical Problems in Theoretical Physics, 420, 10.1007/BFb0013294

1984, Chemical Oscillations, Waves, and Turbulence Chemical Oscillations, Waves, and Turbulence

2000, Physica D, 143, 1, 10.1016/S0167-2789(00)00094-4

2005, Rev. Mod. Phys., 77, 137, 10.1103/RevModPhys.77.137

2016, Phys. Rep., 610, 1, 10.1016/j.physrep.2015.10.008

2004, Europhys. Lett., 68, 603, 10.1209/epl/i2004-10238-x

2005, Phys. Rev. E, 72, 026208, 10.1103/PhysRevE.72.026208

2007, Phys. Rev. E, 75, 066106, 10.1103/PhysRevE.75.066106

2007, Phys. Rev. Lett., 98, 034101, 10.1103/PhysRevLett.98.034101

2002, Phys. Rev. E, 65, 026139, 10.1103/PhysRevE.65.026139

2005, Phys. Rev. E, 72, 047101, 10.1103/PhysRevE.72.047101

2006, Phys. Rev. Lett., 96, 114102, 10.1103/PhysRevLett.96.114102

2007, Eur. Phys. J.: Spec. Top., 143, 19, 10.1140/epjst/e2007-00066-2

2006, Physica D, 224, 27, 10.1016/j.physd.2006.09.029

2008, Phys. Rev. E, 77, 046211, 10.1103/PhysRevE.77.046211

2012, Phys. Rev. E, 85, 016208, 10.1103/PhysRevE.85.016208

1998, Phys. Rev. Lett., 80, 2109, 10.1103/PhysRevLett.80.2109

2002, Phys. Rev. Lett., 89, 054101, 10.1103/PhysRevLett.89.054101

2008, Phys. Lett. A, 372, 2618, 10.1016/j.physleta.2007.11.069

Zhou, 2009, Enhancing synchronization in systems of non-identical Kuramoto oscillators, Complex Sciences: First International Conference, Complex 2009, Shanghai, China, 23–25 February 2009, Revised Papers, Part 2, 1955

2011, Phys. Rev. Lett., 106, 128701, 10.1103/PhysRevLett.106.128701

2013, Sci. Rep., 3, 1281, 10.1038/srep01281

2013, Phys. Rev. E, 88, 042808, 10.1103/PhysRevE.88.042808

2014, Phys. Rev. Lett., 113, 144101, 10.1103/PhysRevLett.113.144101

2015, Phys. Rev. E, 91, 010802, 10.1103/PhysRevE.91.010802

2016, SIAM J. Appl. Math., 76, 1984, 10.1137/16M1075181

2015, Chaos, 25, 053111, 10.1063/1.4921295

2015, Phys. Rev. E, 92, 062801, 10.1103/PhysRevE.92.062801

2009, Adaptive Networks:Theory, Models and Applications

2008, J. R. Soc. Interface, 5, 259, 10.1098/rsif.2007.1229

2013, Comput. Math. Appl., 65, 1645, 10.1016/j.camwa.2012.12.005

2011, Phys. Rev. E, 84, 016116, 10.1103/PhysRevE.84.016116

2013, Phys. Rev. E, 88, 022818, 10.1103/PhysRevE.88.022818

2006, Phys. Rev. Lett., 96, 164102, 10.1103/PhysRevLett.96.164102

2010, Phys. Rev. E, 81, 026201, 10.1103/PhysRevE.81.026201

2009, Phys. Rev. Lett., 102, 034101, 10.1103/PhysRevLett.102.034101

2011, Phys. Rev. E, 84, 066109, 10.1103/PhysRevE.84.066109

2009, BMC Neurosci., 10, 55, 10.1186/1471-2202-10-55

2006, Eur. Phys. J. B - Condens. Matter Complex Syst., 53, 233, 10.1140/epjb/e2006-00362-y

2002, Phys. Rev. E, 65, 041906, 10.1103/PhysRevE.65.041906

2009, Phys. Rev. E, 79, 046105, 10.1103/PhysRevE.79.046105

2008, PLoS One, 3, 1, 10.1371/journal.pone.0002644

2011, Sci. Rep., 1, 99, 10.1038/srep00099

2011, Phys. Rev. Lett., 107, 234103, 10.1103/PhysRevLett.107.234103

1996, Nature, 382, 807, 10.1038/382807a0

2000, Nat. Neurosci., 3, 919, 10.1038/78829

2008, Annu. Rev. Neurosci., 31, 25, 10.1146/annurev.neuro.31.060407.125639

2007, Science, 315, 1262, 10.1126/science.1137450

2010, Front. Comput. Neurosci., 4, 156, 10.3389/fncom.2010.00156

2006, Phys. Rev. Lett., 96, 208701, 10.1103/PhysRevLett.96.208701

2006, Phys. Rev. E, 74, 056108, 10.1103/PhysRevE.74.056108

2000, Phys. Rev. Lett., 84, 6114, 10.1103/PhysRevLett.84.6114

2003, Phys. Rev. E, 67, 066118, 10.1103/PhysRevE.67.066118

2004, Europhys. Lett., 67, 328, 10.1209/epl/i2003-10287-7

2008, Phys. Rev. Lett., 100, 114101, 10.1103/PhysRevLett.100.114101

2006, Cognit. Neurodyn., 1, 39, 10.1007/s11571-006-9006-5

2011, PLOS Comput. Biol., 7, 1, 10.1371/journal/pcbi.1002038

2007, Phys. Rev. E, 76, 016207, 10.1103/PhysRevE.76.016207

2014, Phys. Lett. A, 378, 139, 10.1016/j.physleta.2013.10.031

2012, Phys. Rev. E, 86, 015101, 10.1103/PhysRevE.86.015101

2014, Phys. Rev. E, 89, 032906, 10.1103/PhysRevE.89.032906

2015, Phys. Rev. Lett., 114, 038701, 10.1103/PhysRevLett.114.038701

2015, Europhys. Lett., 111, 50010, 10.1209/0295-5075/111/50010

2016, Sci. Rep., 6, 27111, 10.1038/srep27111

Zhou, 2009, Enhancement of synchronizability of the Kuramoto model with assortative degree-frequency mixing, Complex Sciences: First International Conference, Complex 2009, Shanghai, China, 23–25 February, 2009, Revised Papers, Part 2, 1967

2009, Phys. Rev. E, 80, 066120, 10.1103/PhysRevE.80.066120

2009, Commun. Nonlinear Sci. Numer. Simul., 14, 2536, 10.1016/j.cnsns.2008.09.032

2011, Chaos, 21, 025110, 10.1063/1.3590855

2010, Physica D, 239, 1759, 10.1016/j.physd.2010.05.010

2008, Eur. Phys. J. B, 62, 87, 10.1140/epjb/e2008-00126-9

2015, Phys. Rev. E, 92, 032901, 10.1103/PhysRevE.92.032901

2008, Phys. Rev. E, 78, 016103, 10.1103/PhysRevE.78.016103

2010, Front. Hum. Neurosci., 4, 190, 10.3389/fnhum.2010.00190

2006, Neural Comput., 18, 245, 10.1162/089976606775093882

2014, Cognit. Neurodyn., 8, 479, 10.1007/s11571-014-9288-y

2009, Proc. Natl. Acad. Sci. U.S.A., 106, 10302, 10.1073/pnas.0901831106

2005, Clin. Neurophysiol., 116, 2266, 10.1016/j.clinph.2005.06.011

2005, Phys. Rev. E, 72, 031909, 10.1103/PhysRevE.72.031909

2016, Phys. Rev. E, 94, 042427, 10.1103/PhysRevE.94.042427

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Tập 27 Số 7

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