Exponential synchronization of complex-valued delayed coupled systems on networks with aperiodically on-off coupling

Abstract

In this paper, the exponential synchronization problem of complex-valued delayed coupled systems on networks with aperiodically on-off coupling is investigated. The on-off coupling is aperiodic, which takes the general on-off coupling as a special case. We analyze the complex-valued system directly by using R-Derivative and Conjugate R-Derivative. Then based on the Lyapunov method and graph theory, we give two kinds of synchronization criteria, which have a close relationship with the switch-on width of the coupling and the topological structure of the underlying network. Specially, when the switch-on width tends to zero, on-off coupling becomes impulsive control. Hence, the corresponding synchronization criteria under impulsive control are given as well. To illustrate the practicability of the main results, we apply the derived results to complex-valued delayed coupled oscillators. Finally, two numerical examples are given to verify the validity of the theoretical results.