Hybrid synchronization of identical chaotic systems using sliding mode control and an application to Vaidyanathan chaotic systems

Abstract

Hybrid phase synchronization is a newtype of synchronization of a pair of chaotic systems called the master and slave systems. In hybrid phase synchronization, the odd numbered states of themaster and slave systems are completely synchronized (CS), while their even numbered states are anti-synchronized (AS). The hybrid phase synchronization has applications in secure communications and cryptosystems. This work derives a new result for the hybrid phase synchronization of identical chaotic systems using slidingmode control. Themain result has been proved using Lyapunov stability theory. Slidingmode control (SMC) is well-known as a robust approach and useful for controller design in systems with parameter uncertainties. As an application of this general result, a sliding mode controller is derived for the hybrid phase synchronization of the identical 3-D Vaidyanathan chaotic systems (2014). MATLAB simulations have been provided to illustrate the Vaidyanathan system and the hybrid synchronizer results for the identical Vaidyanathan systems.