Chameleon Chaotic Systems With Quadratic Nonlinearities: An Adaptive Finite-Time Sliding Mode Control Approach and Circuit Simulation

Saleh Mobayen,Afef Fekih,Sundarapandian Vaidyanathan,Aceng Sambas

doi:10.1109/access.2021.3074518

Abstract

A chameleon chaotic system is a chaotic system in which the chaotic attractor can change between hidden and self-excited attractor depending on the values of parameters. In this work, we construct a family of nine new chameleon chaotic systems by introducing two parameters to the 3-D chaotic systems with quadratic nonlinearities and exhibiting line equilibrium points analyzed by Jafari and Sprott (2013). In the analysis of chameleon chaotic flow of the nine new chaotic systems, we discover three categories of hidden attractors (no equilibria, line of equilibria, one stable equilibrium) and a self-excited attractor. The proposed family of nine new chameleon chaotic systems is a novel class of chaotic systems with interesting dynamic properties. Moreover, this study motivates on the adaptive finite time sliding mode control of one category of these chameleon chaotic systems subjected to uncertainties and disturbances. As an engineering application, we have built an electronic circuit design of a new chameleon chaotic system using MultiSim.

Highlights

A chaotic system is a nonlinear dynamical system with three properties, viz. (i) sensitive dependence on initial conditions, (ii) topological transitivity, and (iii) dense periodic points [1]
Mobayen et al.: Chameleon Chaotic Systems With Quadratic Nonlinearities consists of chameleon chaotic systems displaying a line of equilibrium points, stable equilibrium, unstable equilibrium or no equilibrium based on different values of the parameters
We show that the new systems are chameleon chaotic systems, viz. these systems can change between hidden and self-excited attractors depending on the values of the parameters a and b

Summary

INTRODUCTION

A chaotic system is a nonlinear dynamical system with three properties, viz. (i) sensitive dependence on initial conditions, (ii) topological transitivity, and (iii) dense periodic points [1]. Jafari and Sprott [21] found a family of nine chaotic systems with quadratic nonlinearities exhibiting a line of equilibrium points denoted as LE1, LE2, . Whereas the Jafari-Sprott chaotic systems [21] exhibit only a line of equilibrium points, our new family. S. Mobayen et al.: Chameleon Chaotic Systems With Quadratic Nonlinearities consists of chameleon chaotic systems displaying a line of equilibrium points, stable equilibrium, unstable equilibrium or no equilibrium based on different values of the parameters. The discovery of nine new chameleon chaotic systems from the Jafari-Sprott systems [21] is a novelty of our research work.

CHAMELEON CHAOTIC FLOWS

ADAPTIVE FINITE-TIME SLIDING MODE CONTROL

SIMULATION RESULTS

C3R6 X1X2

CONCLUSION