Synchronization of chaotic systems with variable coefficients

Abstract

In this paper, a novel method, to synchronize two identical or different chaotic/hyperchaotic systems with variable coefficients, is proposed based on the strictly positive real transfer function matrix. By adding a synchronization controller to the response system, the nonlinear parts of the error system derived from the synchronized systems are identified as the inputs of the error system, and the error state variables are identified as the outputs of the error system. Then the transfer function matrix of the error system can be strictly positive real. As a result, the error system can be asymptotically stable at the origin, i.e., the two chaotic/hyperchaotic systems can reach stable synchronization. Moreover, the designed synchronization controllers are linear, clear in parameter selections and robust to the changes of the coefficients of the error system. The specific design processes of the synchronization controllers and the corresponding results are presented in the paper. Also, the numerical simulation results are given to verify the feasibility and effectiveness of this method.