Impulsive synchronization and initial value effect for a memristor-based chaotic system

Abstract

Taking Chua's circuit with a smooth cubic flux-controlled memristor as an example, the impulsive control synchronization method for two identical memristor-based chaotic systems is studied. Based on the Lyapunov stability theory, the asymptotic stability condition for the impulsive synchronization of the memristor-based chaotic systems is given. Combining with the maximum conditional Lyapunov exponent spectrum of the error system, effects of the system initial values on the performances of impulsive synchronization are discussed, and corresponding simulation experiments are performed. Results indicate that using impulsive synchronization for the two identical memristor-based chaotic systems is feasible and effective with appropriate impulsive control parameters; the initial values of the memristor-based chaotic systems have some effects on the performances of impulsive synchronization, which can be inhibited by increasing the impulsive coupling strength.