Asymmetric memristive Chua’s chaotic circuits

Abstract

ABSTRACT Asymmetric property of the pinched hysteresis loop usually appears in a real memristor. To imitate this property, an asymmetric memristor emulator is constructed by an analog circuit consisting of a non-balance diode-bridge and a resistor-capacitor (RC) filter. By coupling this emulator to the classical Chua’s circuit in parallel in both forward and reverse ways, two asymmetric memristive Chua’s circuits are proposed and their mathematical models are established. Because of the symmetry between the forward and reverse circuits, the forward memristive Chua’s (FAMC) circuit is focused on modelling the normalised system and investigating the equilibrium stability. With the FAMC system, several numerical plots are employed to discuss the parameter-dependent complex dynamics and initial-dependent coexisting behaviours. The numerical results manifest that there are three equilibrium points in the FAMC system, among which two non-zero equilibrium points are asymmetric, resulting in the emergence of asymmetric attractors. With the change of system parameters, the stability of one non-zero equilibrium point converts from unstable saddle-focus into stable node-focus, leading to the coexistence of multiple attractors. In addition, hardware experiments on a breadboard level are executed and the captured results well verify the numerical plots.