Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors* *Project supported by the National Natural Science Foundation of China (Grant No. 61203004), the Natural Science Foundation of Heilongjiang Province, China (Grant No. F201220), and the Heilongjiang Provincial Natural Science Foundation of Joint Guidance Project (Grant No. LH2020F022).

Abstract

A five-value memristor model is proposed, it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current. Then, based on the classical Liu–Chen system, a new memristor-based four-dimensional (4D) chaotic system is designed by using the five-value memristor. The trajectory phase diagram, Poincare mapping, bifurcation diagram, and Lyapunov exponent spectrum are drawn by numerical simulation. It is found that, in addition to the general chaos characteristics, the system has some special phenomena, such as hidden homogenous multistabilities, hidden heterogeneous multistabilities, and hidden super-multistabilities. Finally, according to the dimensionless equation of the system, the circuit model of the system is built and simulated. The results are consistent with the numerical simulation results, which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.