A Novel Memristor Chaotic System with a Hidden Attractor and Multistability and Its Implementation in a Circuit

Abstract

By introducing an ideal and active flux-controlled memristor and tangent function into an existing chaotic system, an interesting memristor-based self-replication chaotic system is proposed. The most striking feature is that this system has infinite line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. In this paper, bifurcation diagrams and Lyapunov exponential spectrum are used to analyze in detail the influence of various parameter changes on the dynamic behavior of the system; it shows that the newly proposed chaotic system has the phenomenon of alternating chaos and limit cycle. Especially, transition behavior of the transient period with steady chaos can be also found for some initial conditions. Moreover, a hardware circuit is designed by PSpice and fabricated, and its experimental results effectively verify the truth of extreme multistability.