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

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.

Automated summary

This study introduces a family of nine new chameleon chaotic systems, identifies different types of hidden attractors and self-excited attractors, and explores methods for controlling these systems under uncertainties and disturbances.