On a New Three-Dimensional Chaotic System with Adaptive Control and Chaos Synchronization

Abstract

A three-dimensional autonomous deterministic chaotic system having six parameters is explored within this article. The dynamical characteristics of the proposed system are investigated through eigenvalues structure, bifurcation diagrams, Kaplan–Yorke dimension, Lyapunov exponents, time response, and phase plane trajectories. For the suitable design of the system parameters, it is found that the system can exhibit periodic, period-n, or chaotic oscillations. Accordingly, the system’s dynamical behavior to the variation of its coefficients has been explored. The obtained results revealed that the proposed dynamical system does not lose its chaotic oscillations for the small fluctuations of one or more of the values of its parameters. In addition, chaos control and chaos synchronization have been studied by means of the adaptive control strategy relying on Lyapunov’s second method of stability. The numerical simulation revealed that superior chaos control and master-slave synchronization have been achieved by the applied control laws. Finally, the obtained results have been simulated via a nonlinear electronic circuit that demonstrated the feasibility of the purposed chaotic system for different engineering applications such as secure communications, cryptosystems, image encryption, and image processing.