Synchronization of hyperchaotic harmonics in time-delay systems and its application to secure communication

We present a predictor-feedback method for synchronizing chaotic systems in this paper. By using this method, two structurally equivalent or nonequivalent systems can be synchronized very effectively and quickly. Moreover, the feedback perturbation can be switched on even if trajectories of the two systems are far from each other. Therefore, this method is applicable to real-world experimental systems, especially to some fast experimental systems. The validity of this method is demonstrated by synchronizing hyperchaotic harmonics in a time-delay system. As an application, we introduce how messages can be encoded, transmitted, and decoded using this technique. We suggest taking use of the multistability of time-delay systems to improve the performance of the secure communication.