Simple Synchronization Scheme for a Class of Nonlinear Chaotic Systems Using a Single Input Control

Abstract

An increasing concern in the analysis of chaotic and hyperchaotic systems, as well as the phenomena of synchronization connected with them, has brought a boom in the field of nonlinear dynamics. The present work discusses a generic approach to the synchronization challenges in a drive-response setup for a class of nonlinear chaotic as well as hyperchaotic systems. Generally, it is difficult to synchronize chaotic systems using a single input control and it becomes much more difficult in case of higher dimensional chaotic/hyperchaotic systems. In the present manuscript, a single input control on the basis of Lyapunov’s stability theorem is deployed to synchronize two chaotic/hyperchaotic systems in drive-response configuration. The single input feedback controller thus devised confirms that the state variables of the response system synchronize with the corresponding state variables of the drive system. Using Lyapunov’s stability analysis, required conditions have been derived so as to accomplish the task of synchronization in a simple manner. To verify the efficacy of the proposed control law, chaotic systems such as Lorenz-Stenflo hyperchaotic systems, Modified Lorenz-Stenflo chaotic systems and Lorenz chaotic systems have been considered. Finally, numerical simulations to validate the analytical results have been presented.