Reduced Order Synchronization of Two Different Chaotic Systems Using Nonlinear Active Control with or without Time Delay

Abstract

In this article, a nonlinear active control technique is proposed so as to attain the synchronization of two different chaotic systems. Master and slave configuration is incorporated for the analysis. The main objective is to design Reduced Order Synchronization (ROS) scheme, where the order of the master system is greater than that of the slave system. Initially, active control technique based ROS is achieved and after that the results are extended to address reduced order synchronization in the presence of time delays in the systems. Based on Routh-Hurwitz criterion and Lyapunov stability theorem, the convergent behaviour of the error dynamics is proved. The theoretical results are validated by the detailed simulation results for Lorenz-Stenflo and Lü system.