Novel chaotic behavior in the Muthuswamy-Chua system using Chebyshev Polynomials

Abstract

In this paper, three kinds of memristors with memristance functions obtained from the Chebyshev polynomials are used in the Muthuswamy-Chua system, which has only three circuit elements: a linear passive inductor, a linear passive capacitor and a nonlinear active memristor. We use multivariable second-order polynomial functions of current and memristor state for the internal state function of the memristor. This enables our system to generate not only double-scroll but also four-scroll attractors. Systematic studies of chaotic behavior in these systems are performed using phase portraits, bifurcation diagrams and Lyapunov exponents. Simulation results show that all these systems exhibit chaotic behavior over a range of control parameters. Copyright © 2014 John Wiley & Sons, Ltd.