Complex Oscillations of Chua Corsage Memristor with Two Symmetrical Locally Active Domains

Abstract

This paper proposes a modified Chua Corsage Memristor endowed with two symmetrical locally active domains. Under the DC bias voltage in the locally active domains, the memristor with an inductor can construct a second-order circuit to generate periodic oscillation. Based on the theories of the edge of chaos and local activity, the oscillation mechanism of the symmetrical periodic oscillations of the circuit is revealed. The third-order memristor circuit is constructed by adding a passive capacitor in parallel with the memristor in the second-order circuit, where symmetrical periodic oscillations and symmetrical chaos emerge either on or near the edge of chaos domains. The oscillation mechanisms of the memristor-based circuits are analyzed via Domains distribution maps, which include the division of locally passive domains, locally active domains, and the edge of chaos domains. Finally, the symmetrical dynamic characteristics are investigated via theory and simulations, including Lyapunov exponents, bifurcation diagrams, and dynamic maps.

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

“…Its rich nonlinear behavior and malleable have been widely used in recent years, including the design of memristor circuits with diferent orders and the construction of circuit models [9][10][11][12]. As a nonlinear dual-port element, memristor is added to the classical nonlinear system, such as Chua's circuit [13], Lorenz system [14], and Chen's system [15]. 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.…”

“…As a nonlinear dual-port element, memristor is added to the classical nonlinear system, such as Chua's circuit [13], Lorenz system [14], and Chen's system [15]. 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.…”