Generalized outer synchronization between non-dissipatively coupled complex networks with different-dimensional nodes

Abstract

• Asymptotic and exponential generalized outer synchronization criteria are proposed. • Only partial dynamics of each node in the response network is constrained by QUAD. • Our network nodes may be non-dissipatively coupled and have different dimensions. • Our network models possess different time-varying coupling configurations. • Our networks have nonlinear inner functions and different time-varying delays. This paper investigates the generalized outer synchronization (GOS) between two non-dissipatively coupled complex dynamical networks (CDNs) with different time-varying coupling delays. Our drive-response networks also possess nonlinear inner coupling functions and time-varying outer coupling configuration matrices. Besides, in our network models, the nodes in the same network are nonidentical and the nodes in different networks have different state dimensions. Asymptotic generalized outer synchronization (AGOS) and exponential generalized outer synchronization (EGOS) are defined for our CDNs. Our main objective in this paper is to design AGOS and EGOS controllers for our drive-response networks via the open-plus-closed-loop control technique. Distinguished from most existing literatures, it is the partial intrinsic dynamics of each node in response network that is restricted by the QUAD condition, which is easy to be satisfied. Representative simulation examples are given to verify the effectiveness and feasibility of our GOS theoretical results in this paper.