Adaptive coupling induced multi-stable states in complex networks

Physica D: Nonlinear Phenomena

Volumn 267, Issue , 2014, Pages 36-48

  Chandrasekar, V K ^a   Sheeba, Jane H ^a   Subash, B ^a   Lakshmanan, M ^a   Kurths, J ^b  

^a BHARATHIDASAN UNIVERSITY   (India)

^b POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

Author keywords

Adaptive coupling; Complex networks; Synchronization

Indexed keywords

COMPLEX NETWORKS; PLASTICITY TESTING; SYNCHRONIZATION;

ADAPTIVE COUPLING; ANALYTICAL RESULTS; ASYMPTOTICALLY STABLE; CLUSTER SYNCHRONIZATION; DESYNCHRONIZATION; NON-IDENTICAL OSCILLATORS; PHASE OSCILLATORS; PHASE RELATIONSHIPS;

ADAPTIVE CONTROL SYSTEMS;

EID: 84889087759     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2013.08.013     Document Type: Article

References (67)

1. A.T. Winfree Biological rhythms and the behavior of populations of coupled oscillators J. Theoret. Biol. 16 1967 15
2. Y. Kuramoto Chemical Oscillations, Waves, and Turbulence 1984 Springer-Verlag Berlin
3. A. Pikovsky, M. Rosenblum, and J. Kurths Synchronization - A Universal Concept in Nonlinear Sciences 2001 Cambridge University Press Cambridge
4. S.H. Strogatz Exploring complex networks Nature 410 2001 268
5. W. Singer Neuronal synchrony: a versatile code for the definition of relations? Neuron 24 1999 49
6. P. Fries A mechanism for cognitive dynamics: neuronal communication through neuronal coherence Trends. Cogn. Sci. 9 2005 474
7. Y. Yamaguchi, N. Sato, H. Wagatsuma, Z. Wu, C. Molter, and Y. Aota A unified view of theta-phase coding in the entorhinal-hippocampal system Curr. Opin. Neurobiol. 17 2007 197
8. Jane H. Sheeba, A. Stefanovska, and P.V.E. McClintock Neuronal synchrony during anesthesia: a thalamocortical model Biophys. J. 95 2008 2722
9. L. Timmermann, J. Gross, M. Dirks, J. Volkmann, H. Freund, and A. Schnitzler The cerebral oscillatory network of parkinsonian resting tremor Brain 126 2003 199
10. J.A. Goldberg, T. Boraud, S. Maraton, S.N. Haber, E. Vaadia, and H. Bergman Enhanced synchrony among primary motor cortex neurons in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine primate model of Parkinson's disease J. Neurosci. 22 2002 4639
11. B. Percha, R. Dzakpasu, and M. Zochowski Transition from local to global phase synchrony in small world neural network and its possible implications for epilepsy Phys. Rev. E. 72 2005 031909
12. M. Zucconi, M. Manconi, D. Bizzozero, F. Rundo, C.J. Stam, L. Ferini-Strambi, and R. Ferri EEG synchronisation during sleep-related epileptic seizures as a new tool to discriminate confusional arousals from paroxysmal arousals: preliminary findings Neurol. Sci. 26 2005 199
13. G. Pfurtscheller, and C. Neuper Event-related synchronization of mu rhythm in the EEG over the cortical hand area in man Neurosci. Lett. 174 1994 93
14. C.M. Krause, H. Lang, M. Laine, and B. Pörn Event-related. EEG desynchronization and synchronization during an auditory memory task Electroencephalogr. Clin. Neurophysiol. 98 1996 319
15. L. Leocani, C. Toro, P. Manganotti, P. Zhuang, and M. Hallet Event-related coherence and event-related desynchronization/synchronization in the 10 Hz and 20 Hz EEG during self-paced movements Electroencephalogr. Clin. Neurophysiol. 104 1997 199 206 (Pubitemid 27242496)
16. G. Pfurtschelle, and F.H. Lopes da Silva Event-related EEG/MEG synchronization and desynchronization: basic principles Clin. Neurophysiol. 110 1999 1842
17. Jane H. Sheeba, V.K. Chandrasekar, and M. Lakshmanan Event-related desynchronization in diffusively coupled oscillator models Phys. Rev. Lett. 103 2009 074101
18. J. Acebron, L. Bonilla, C. Perez Vicente, F. Ritort, and R. Spigler The Kuramoto model: a simple paradigm for synchronization phenomena Rev. Modern Phys. 77 2005 137
19. R. Albert, and A.-L. Barabasi Statistical mechanics of complex networks Rev. Modern Phys. 74 2002 47
20. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang Complex networks: structure and dynamics Phys. Rep. 424 2006 175
21. L. Wu, S. Zhu, and X. Luo Diversity-induced resonance on weighted scale-free networks Chaos 20 2010 033113
22. M. Perc Stochastic resonance on excitable small-world networks via a pacemaker Phys. Rev. E 76 2007 066203
23. P. Seliger, S.C. Young, and L.S. Tsimring Plasticity and learning in a network of coupled phase oscillators Phys. Rev. E 65 2002 041906
24. D.H. Zanette, and A.S. Mikhailov Dynamical clustering in oscillator ensembles with time-dependent interactions Europhys. Lett. 65 2004 465
25. M.G. Zimmermann, V.M. Eguiluz, and M. San Miguel Coevolution of dynamical states and interactions in dynamic networks Phys. Rev. E 69 2004 065102
26. J.M. Pacheco, A. Traulsen, and M.A. Nowak Co-evolution of strategy and structure in complex networks with dynamical linking Phys. Rev. Lett. 97 2006 258103
27. N. Masuda, and H. Kori Formation of feedforward networks and frequency synchrony by spike-timing-dependent plasticity J. Comput. Neurosci. 22 2007 327
28. Y.L. Maistrenko, B. Lysyansky, C. Hauptmann, O. Burylko, and P.A. Tass Multistability in the Kuramoto model with synaptic plasticity Phys. Rev. E 75 2007 066207
29. H. Cateau, K. Kitano, and T. Fukai Interplay between a phase response curve and spike-timing-dependent plasticity leading to wireless clustering Phys. Rev. E 77 2008 051909
30. M. Chen, Y. Shang, Y. Zou, and J. Kurths Synchronization in the Kuramoto model: a dynamical gradient network approach Phys. Rev. E 77 2008 027101
31. M. Gilson, A.N. Burkitt, D.B. Grayden, D.A. Thomas, and J.L. van Hemmen Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks III: partially connected neurons driven by spontaneous activity Biol. Cybernet. 101 2009 411
32. A. Szolnoki, and M. Perc Resolving social dilemmas on evolving random networks Europhys. Lett. 86 2009 30007
33. A. Szolnoki, and M. Perc Emergence of multilevel selection in the prisoner's dilemma game on coevolving random networks New J. Phys. 11 2009 093033
34. J. Poncela, J. Gomez-Gardenes, A. Traulsen, and Y. Moreno Evolutionary game dynamics in a growing structured population New J. Phys. 11 2009 083031
35. M. Perc, and A. Szolnoki Coevolutionary games - a mini review Biosystems 99 2010 109
36. M. Iwasa, K. Iida, and D. Tanaka Hierarchical cluster structures in a one-dimensional swarm oscillator model Phys. Rev. E 81 2010 046220
37. M. Iwasa, and D. Tanaka Dimensionality of clusters in a swarm oscillator model Phys. Rev. E 81 2010 066214
38. G.Q. Bi, and M.M. Poo Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type J. Neurosci. 18 1998 10464
39. H. Markram, J. Lubke, M. Frotscher, and B. Sakmann Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs Science 275 1997 213
40. N. Caporale, and Y. Dan Spike timing-dependent plasticity: a Hebbian learning rule Annu. Rev. Neurosci. 31 2008 25
41. C.S. Zhou, and J. Kurths Dynamical weights and enhanced synchronization in adaptive complex networks Phys. Rev. Lett. 96 2006 164102
42. Q. Ren, and J. Zhao Adaptive coupling and enhanced synchronization in coupled phase oscillators Phys. Rev. E 76 2007 016207
43. J.L. Hou, and J. Zhao The order-oscillation induced by negative feedback in the adaptive scheme Phys. Lett. A 374 2010 929 932
44. V.K. Chandrasekar, Jane H. Sheeba, and M. Lakshmanan Mass synchronization: occurrence and its control with possible applications to brain dynamics Chaos 20 2010 045106
45. T. Aoki, and T. Aoyagi Co-evolution of phases and connection strengths in a network of phase oscillators Phys. Rev. Lett. 102 2009 034101
46. T. Aoki, and T. Aoyagi Self-organized network of phase oscillators coupled by activity-dependent interactions Phys. Rev. E 84 2011 066109
47. W. Yuan, and C. Zhou Interplay between structure and dynamics in adaptive complex networks: emergence and amplification of modularity by adaptive dynamics Phys. Rev. E 84 2011 016116
48. J. Zhu, M. Zhao, W. Yu, C. Zhou, and B. Wang Better synchronizability in generalized adaptive networks Phys. Rev. E 81 2010 026201
49. M.S. Lama, J.M. Lopez, and H.S. Wio Spontaneous emergence of contrarian-like behaviour in an opinion spreading model Europhys. Lett. 72 2005 851
50. Guven Demirel, Roshan Prizak, P. Nitish Reddy, and Thilo Gross Opinion formation and cyclic dominance in adaptive networks arXiv:1011.1124
51. Alessandro Pluchino, Stefano Boccaletti, Vito Latora, and Andrea Rapisarda Opinion dynamics and synchronization in a network of scientific collaborations Physica A 372 2006 316
52. C. Furusawa, and K. Kaneko Zipf's law in gene expression Phys. Rev. Lett. 90 2003 088102
53. S. Jain, and S. Krishna A model for the emergence of cooperation, interdependence, and structure in evolving networks Proc. Natl. Acad. Sci. USA 98 2001 543
54. A. Tero, S. Takagi, T. Saigusa, K. Ito, D.P. Bebber, M.D. Fricker, K. Yumiki, R. Kobayashi, and T. Nakagaki Rules for biologically inspired adaptive network design Science 327 2010 439
55. K.D. Harris, J. Csicsvari, H. Hirase, G. Dragoi, and G. Buzsaki Organization of cell assemblies in the hippocampus Nature (London) 424 2003 552
56. T. Gross, and B. Blasius Adaptive coevolutionary networks: a review J. R. Soc. Interface 5 2008 259
57. Daniel M. Abrams, Rennie Mirollo, Steven H. Strogatz, and Daniel A. Wiley Solvable model for chimera states of coupled oscillators Phys. Rev. Lett. 101 2008 084103
58. H. Hong, and S.H. Strogatz Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators Phys. Rev. Lett. 106 2011 054102
59. H. Hong, and S.H. Strogatz Conformists and contrarians in a Kuramoto model with identical natural frequencies Phys. Rev. E 84 2011 046202
60. D. Wu, S. Zhu, X. Luo, and L. Wu Effects of adaptive coupling on stochastic resonance of small-world networks Phys. Rev. E 84 2011 021102
61. D. Huang Synchronization in adaptive weighted networks Phys. Rev. E 74 2006 046208
62. M. Li, X. Wang, Y. Fan, Z. Di, and C. Lai Onset of synchronization in weighted complex networks: the effect of weight-degree correlation Chaos 21 2011 025108
63. Tae-Wook Ko, and G. Bard Ermentrout Partially locked states in coupled oscillators due to inhomogeneous coupling Phys. Rev. E 78 2008 016203
64. T. Tanaka, and T. Aoyagi Multistable attractors in a network of phase oscillators with three-body interactions Phys. Rev. Lett. 106 2011 224101
65. E.M. Izhikevich Phase models with explicit time delays Phys. Rev. E 58 1998 905
66. Steven H. Strogatz From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators Physica D 143 2000 1 20
67. Gabriel H. Paissan, and Damian H. Zanette Synchronization of phase oscillators with heterogeneous coupling: a solvable case Physica D 237 2008 818 828 (Pubitemid 351514794)