A New 3-D Chaotic System with an Ellipse of Equilibrium Points and its Adaptive Synchronization - Sundarapandian Vaidyanathan, Aceng Sambas, Djoni Hatidja, Jullia Titaley, Mohamad Afendee Mohamed, Mustafa Mamat (International Journal of Advanced Science and Technology, 2020)
A new 3-D chaotic system with an ellipse of equilibrium points is proposed in this work. There is great interest in the literature in discovering chaotic systems with closed curves of equilibrium points. In this work, we report a new 3-D chaotic system with an ellipse of   equilibrium points in the (x, y)-plane. We perform a detailed dynamic analysis of the chaotic system with Lyapunov exponents, phase portraits, etc. We show that the new chaotic system is multi-stable with coexisting chaotic attractors. As a control application, we apply adaptive control to derive new results for the global chaos synchronization of the new chaotic system with itself. Adaptive control results are established using Lyapunov stability theory. MATLAB simulations are shown to illustrate the synchronization results.  Keywords: chaotic system, ellipse of equilibrium, dynamical analysis, synchronization