Analysis and electronic implementation of an absolute memristor autonomous Van der Pol-Duffing circuit

Abstract

In this paper, a memristor-based chaotic circuit is built by replacing the nonlinear resistor of a unified Van der Pol-Duffing circuit by an ideal and active flux-controlled memristor with an absolute value nonlinearity. The equilibrium points of the mathematical model describing the proposed absolute memristor Van der Pol-Duffing circuit are determined and their stabilities are analyzed thank to the Routh-Hurwitz criteria. The numerical simulations reveal that the proposed absolute memristor circuit exhibits reverse period-doubling to chaos, bistable one-scroll chaotic attractors, double-scroll chaotic attractor, bistable periodic attractors and antimonotonicity phenomenon. Moreover the proposed absolute memristor circuit is implemented in PSIM software package. The results found using the PSIM software package have a good qualitative agreement with those found during the numerical simulations.