摘要
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.
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.
基金
the Science and Technology R&D Program of Zhejiang Province (No.2007C33071).
