Global Chaos Synchronization of Liu-Yang Systems via Sliding Mode Control

This research work investigates the global chaos synchronization of identical chaotic systems based on sliding mode control theory and Lyapunov stability theory. The paper begins with a problem statement on global chaos synchronization of chaotic systems. A general result is derived for the global chaos synchronization of chaotic systems using slide mode control and this result is established using Lyapunov stability theory. Next, as an application of this general result, a sliding mode controller is derived for the global chaos synchronization of identical Liu-Yang chaotic systems (2010). Liu-Yang system is a new Lorenz-like chaotic system, which has very different fixed points: one saddle and two stable node-foci. Hence, this new chaotic system is topologically non-equivalent to Lorenz and other Lorenz-like systems. Moreover, in the sense defined by Vaněček and Čelikovský (1996), the Liu-Yang system (2010) connects the original Lorenz system (1964) and the original Chen system (1999) and represents a transition from one to the other. MATLAB simulations are shown to illustrate the sliding controller design for the global chaos synchronization of identical Liu-Yang chaotic systems. Keywords— Chaos, chaotic systems, synchronization, sliding mode control, Lyapunov stability theory, Liu-Yang system.