Abstract.
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance their mutual synchronization. We show that the evolving network reaches a small-world structure. Its clustering coefficient attains a maximum for an intermediate intensity of the coupling between oscillators, where a rich diversity of synchronized oscillator groups is observed. In the stationary state, these synchronized groups are directly associated with network clusters.
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References
N. Wiener, Cybernetics, or Control and Communication in the Animal and the Machine (MIT Press, Cambridge, 1948)
A.T. Winfree, J. Theor. Biol. 16, 15 (1967)
C.M. Gray, P. König, A. Engel, W. Singer, Nature 338, 334 (1989)
S.H. Strogatz, Sync. The Emerging Science of Spontaneous Order (Hyperion, New York, 2003)
J. Buck, E. Buck, Science 159, 1319 (1968)
J. Buck, E. Buck, Sci. Am. 234, 74 (1976)
S.H. Strogatz, D.M. Abrams, A. McRobie, B. Eckhardt, E. Ott, Nature 438, 43 (2005)
L.G. Moyano, G. Abramson, D.H. Zanette, Eur. Phys. J. B 22, 223 (2001)
M. Ipsen, A.S. Mikhailov, Phys. Rev. E 66, 046109 (2002)
P. Gong, C. Van Leeuwen, Europhys. Lett. 67, 328 (2004)
Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Berlin, 1984)
J.A. Acebrón, L.L. Bonilla, C.J. Pérez Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005)
S.C. Manrubia, A.S. Mikhailov, D.H. Zanette, Emergence of Dynamical Order. Synchronization Phenomena in Complex Systems (World Scientific, Singapore, 2004)
D. Van Den Berg, C. Van Leeuwen, Europhys. Lett. 65, 459 (2004)
H. Hong, M.Y. Choi, B.J. Kim Phys, Rev. E 65, 026139 (2002)
T. Ichinomiya, Phys. Rev. E 70, 026116 (2004)
D.-S. Lee, Phys. Rev. E 72, 026208 (2005)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
P.N. McGraw, M. Menzinger, Phys. Rev. E 72, 015101 (2005)
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Gleiser, P., Zanette, D. Synchronization and structure in an adaptive oscillator network. Eur. Phys. J. B 53, 233–238 (2006). https://doi.org/10.1140/epjb/e2006-00362-y
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DOI: https://doi.org/10.1140/epjb/e2006-00362-y