Cluster synchronization in oscillatory networks.
Synchronous behavior in networks of coupled oscillators is a commonly observed phenomenon attracting a growing interest in physics, biology, communication, and other fields of science and technology. Besides global synchronization, one can also observe splitting of the full network into several clusters of mutually synchronized oscillators. In this paper, we study the conditions for such cluster partitioning into ensembles for the case of identical chaotic systems. We focus mainly on the existence and the stability of unique unconditional clusters whose rise does not depend on the origin of the other clusters. Also, conditional clusters in arrays of globally nonsymmetrically coupled identical chaotic oscillators are investigated. The design problem of organizing clusters into a given configuration is discussed.
Belykh
Vladimir N
VN
Department of Mathematics, Volga State Academy, 5, Nesterov Str., 603000 Nizhny Novgorod, Russia.
Osipov
Grigory V
GV
Petrov
Valentin S
VS
Suykens
Johan A K
JA
Vandewalle
Joos
J
D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D016000:Cluster Analysis; D003198:Computer Simulation; D005246:Feedback; D053858:Metabolic Networks and Pathways / Q000502:physiology*; D008962:Models, Theoretical; D009415:Nerve Net / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*