Summary
Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications
2012
Session Number:A1L-D
Session:
Number:65
Loop structure and cluster synchronization of dynamical networks with time-delayed couplings
Wolfgang Kinzel, Ido Kanter,
pp.65-65
Publication Date:
Online ISSN:2188-5079
Summary:
Nonlinear networks with time-delayed couplings can synchronize to a common chaotic trajectory. If the delay time is larger than the internal time scales of the individual units, the stability of chaos synchronization is determined by the eigenvalue gap of the coupling matrix and the maximal Lyapunov exponent of a corresponding single unit with self-feedback. The eigenvalue gap is related to the global loop structure of the graph of the network, in particular to the greatest common divisor (GCD) of the lengths of the loops. The GCD determines the number of synchronized clusters, as well. We demonstrate this effect for iterated maps, semiconductor lasers and linear stochastic networks.
References:
Synchronization of unidirectional time delay chaotic networks and the greatest common divisor
I. Kanter, M. Zigzag, A. Englert, F. Geissler and W. Kinzel EPL, 93 (2011) 60003