Pinning synchronization of complex networks with time-varying outer coupling and nonlinear multiple time-varying delay coupling

Abstract

This article studies the pinning control problem for complex networks with time-varying outer coupling and nonlinear multiple time-varying delay coupling. The design aim is to provide appropriate pinning feedback controllers such that the nodes converge to the consistent state as well as the equilibrium point, periodic orbit or chaotic orbit of the nonlinear part of the node dynamic. Based on Lyapunov function theory, appropriate positive-definite functions are constructed, and sufficient synchronization criteria for two kinds of complex networks with different time-varying delay coupling are obtained respectively. Meanwhile, the boundary of the time-varying outer coupling and its influence on the synchronization are investigated. The theoretical results are extended to complex networks with general time-varying delay coupling. Simulation results on complex networks consisting of six nonidentical Chua’s circuits with time-varying outer coupling and nonlinear multiple time-varying delay coupling are presented to demonstrate the effectiveness of the proposed approaches.