Generalized synchronization of delayed complex-valued dynamical networks via hybrid control

Abstract

This paper investigates generalized synchronization of drive–response complex-valued dynamical networks (CVDNs) with time-delay. An effective hybrid controller is designed in the complex field to construct response complex-valued networks for achieving generalized synchronization with drive delayed CVDNs. By employing the Lyapunov method in the complex field, an improved impulsive delay differential inequality and the comparison principle for impulsive systems, some generalized synchronization criteria are established under the proposed hybrid controller. Furthermore, the concepts of average impulsive interval and average impulsive gain are applied to deal with the situation that synchronizing impulses and desynchronizing impulses simultaneously exist in the same impulsive sequence. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.