Mixed outer synchronization of two coupled complex networks with time-varying delay coupling and non-delay coupling

Abstract

In this paper, mixed outer synchronization between two different complex dynamical networks without and with time-varying delayed couplings is investigated. By pinning only a fraction of the nodes in the response network, some effective mixed outer synchronization criteria are obtained based on the Lyapunov stability theory. As a result, the mixed outer synchronization between two complex networks is achieved. Then, in the view of the generalized time-varying delayed different inequalities, some sufficient conditions for mixed outer exponential synchronization are derived by imposing the impulsive controllers to the nodes of the corresponding response network. Finally, some numerical simulations are presented to demonstrate the effectiveness and feasibility of the results we obtained in this paper.