Synchronization with on-off coupling: Role of time scales in network dynamics

Abstract

We consider the problem of synchronizing a general complex network by means of the on-off coupling strategy; in this case, the on-off time scale is varied from a very small to a very large value. In particular, we find that when the time scale is comparable to that of node dynamics, synchronization can also be achieved and greatly optimized for the upper bound of the stability region which nearly disappears, and the synchronization speed is accelerated a lot, independent of network topologies. Our study indicates that the time scale for network variation is of crucial importance for network dynamics and synchronization under the comparable time scale which is much more advantageous over other time scales. Both analysis and experiments confirm the conclusions.

Theoretical analysis of synchronization in delayed complex dynamical networks with discontinuous coupling

“…The theoretical result proposed in Corollary 1 is valid for both the fast switching case and the slow switching case. Therefore, our results provide a direct analytical explanation for the synchronization observed in recent numerical simulations of network synchronization without time delays [36,37]. The results in this paper complement and extend existing results.…”

“…[36,37] only for the fast switching case. The theoretical result proposed in Corollary 1 is valid for both the fast switching case and the slow switching case.…”

“…[36,37], the network (2) contains three kind of time scales, i.e., the dynamical time scale for oscillators, the time scales for the on-off coupling, and the time delay of node dynamics.…”

“…Therefore, extending these continuously coupled complex networks to ones that contain discontinuous coupling is needed. Only recently, Chen et al [36,37] investigated the synchronization problem of complex networks with on-off coupling. For the fast switching case, sufficient conditions for the synchronization are given.…”

Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays

“…In [9], it has been found that, for ensembles of yeast transcriptional network, those with deterministic Boolean rules are remarkably stable and those with random Boolean rules are only marginally stable. For various complex/neural/biological networks with deterministic switching topologies, we refer the readers to [2], [5], [30], and [35] for some representative publications.…”