Synchronization criteria based on a general complex dynamical network model
Jianlin Zhang · 重庆大学学报：英文版 · 2008
Many complex dynamical networks display synchronization phenomena. We introduce a general complex dynamical network model. The model is equivalent to a simple vector model of adopting the Kronecker product. Some synchronization criteria,including time-variant networks and time-varying networks,are deduced based on Lyapunov’s stability theory,and they are proven on the condition of obtaining a certain synchronous solution of an isolated cell. In particular,the inner-coupling matrix directly determines the synchronization of the time-invariant network; while for a time-varying periodic dynamical network,the asymptotic stability of a synchronous solution is determined by a constant matrix which is related to the fundamental solution matrices of the linearization system. Finally,illustrative examples are given to validate the results.