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

In this paper, a new chaotic system with three sinusoidal nonlinearitiesis reported. The basic behavior of the new chaotic system is analyzed bymeans of equilibrium points, stability and Lyapunov exponents. The newsystem has countably infinite number of equilibrium points, which is anovel feature of the system. The new system has multiple interestingfeatures 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 suchas bifurcation diagrams, Lyapunov exponent plots and attractor diagrams.The bifurcation analysis and simulation results show that the proposedsystem has rich chaotic dynamics. Furthermore, the adaptive control andsynchronization of the new system are achieved using nonlinear feedbackcontrol methodology. MATLAB plots are shown to illustrate the controlresults for the new chaotic system with three sinusoidal nonlinearities