A New DC Offset Boostable Chaotic System with Multistability, Coexisting Attractors and Its Adaptive Synchronization

Abstract

In this paper, a new chaotic system with three sinusoidal nonlinearities is reported. The basic behavior of the new chaotic system is analyzed by means of equilibrium points, stability, and Lyapunov exponents. The new system has countably infinite number of equilibrium points, which is a novel feature of the system. The new system has multiple interesting features such as topologically different attractors, coexisting attractors, offset-boosted attractors, and polarity reversed offset-boosting attractors. These special features are analyzed and verified using classical tools such as bifurcation diagrams, Lyapunov exponent plots, and attractor diagrams. The bifurcation analysis and simulation results show that the proposed system has rich chaotic dynamics. Furthermore, the adaptive synchronization of the new system is achieved using a nonlinear feedback control methodology. MATLAB plots are shown to illustrate the control results for the new chaotic system with three sinusoidal nonlinearities.