Chaos Synchronization Based on Linear and Adaptive Controls: Theory and Experiment

Abstract

I. Olusola*, R. T. Ogundare, A. I. Egunjobi, E. O. Odufuwa, M. O. Esan,and E. Vincent

In this paper, we report on the theoretical and experimental investigation of chaotic synchronization using a single variable linear feedback and adaptive controllers. Based on the Lyapunov stability theory, theoretical approaches to the design of controls are presented, and the results are validated numerically and by employing electronic circuit experiments. We used two typical oscillators, namely, the Lorenz and Sprott chaotic systems to demonstrate our results; while off-the-shelf components on breadboard were used to experimentally implement the proposed single variable controllers. We specifically show that synchronization of two chaotic systems can be experimentally realized when the strength of the feedback exceeds a theoretically determined threshold.