Dynamical behavior, chaos control and synchronization of a memristor-based ADVP circuit

This paper is devoted to study the dynamical behavior of a modified Autonomous Van der Pol-Duffing (ADVP) circuit when its nonlinear element is replaced by a flux controlled memristor. The bifurcation diagrams, Lyapunov exponents, and phase portraits of the state variables are presented. Then, the chaos which appears at certain values of the system’s parameters is controlled using linear feedback control. Finally, the synchronization between two chaotic modified ADVP circuits is achieved in the case of fully unknown parameters of the system using adaptive synchronization.

► The ADVP circuit is modified by adding a memristor.
► This model has chaos that exists over a wide range of parameters.
► The chaos control and synchronization are presented.