Adaptive Control, Synchronization and Circuit Simulation of a Memristor-Based Hyperchaotic System With Hidden Attractors

Abstract

Memristor-based systems and their potential applications, in which memristor is both a nonlinear element and a memory element, have been received significant attention in the control literature. In this work, we study a memristor-based hyperchaotic system with hidden attractors. First, we study the dynamic properties of the memristor-based hyperchaotic system such as equilibria, Lyapunov exponents, Poincare map, etc. We obtain the Lyapunov exponents of the memristor-based system as \(L_1 = 0.1244\), \(L_2 = 0.0136\), \(L_3 = 0\) and \(L_4 = -10.8161\). Since there are two positive Lyapunov exponents, the memristor-based system is hyperchaotic. Also, the Kaplan-Yorke fractional dimension of the memristor-based hyperchaotic system is obtained as \(D_{KY} = 3.0128\). Next, we design adaptive control and synchronization schemes for the memristor-based hyperchaotic system. The main adaptive control and synchronization results are established using Lyapunov stability theory. MATLAB simulations are shown to illustrate all the main results of this work. Finally, an electronic circuit emulating the memristor-based hyperchaotic system has been designed using off-the-shelf components.