Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors*

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 fourdimensional (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.

Analysis of a time-dependent memristor-based chaotic system and its application in image encryption

“…Memristors are the fourth basic circuit component with natural memory function, and their appearance supplements the relationship between basic variable charges and magnetic flux in circuit theory [1]. Since a physical model of memristor was developed by Hewlett-Packard [2] in 2008, it has been widely introduced into chaotic systems due to the inherent nonlinearity of memristors [3][4][5][6][7][8][9][10][11][12][13]. Numerous studies have shown that chaotic systems based on memristors exhibit rich dynamic behaviors.…”

Complex Dynamic Analysis, Circuit Design and Simplified Predefined Time Synchronization for a Jerk Absolute Memristor Chaotic System

“…Te memristor circuit composed of various classical nonlinear circuits shows colorful and unforgettable dynamic behaviors, including hidden attractors [16][17][18], hyperchaotic behaviors [19], symmetric attractors [13], and extreme multistability [20][21][22][23] with infnite number of coexistence attractors. Te memristor model described by piecewise linear function [24], quadratic nonlinear function [25], and cubic nonlinear function [26] is a mathematical model often used by scholars. Diferent from the previous ones, this paper attempts to introduce a novel and interesting magnetic fux memristor model with absolute value function.…”

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

“…The classical Shilnikov's theorem [9] deems that the chaotic system has at least one unstable equilibrium point. However, in recent years, many researchers have found a class of system that has only a stable equilibrium point, no equilibrium points, or an infinite number of equilibrium points where chaotic oscillations are still present, [10][11][12][13] for there exist hidden attractors in these systems. [14] The existence of hidden attractors increased the uncertainty of the system, so the system could suddenly switch to unexpected attractors under slight perturbations and such a transition could lead to disastrous consequences.…”