Detecting Cluster Synchronization in Chaotic Dynamic Networks via Information Theoretic Measures

Abstract

Sub-systems in a network of chaotic dynamic systems can form clusters of synchronization. In this study, we investigate the problem of detection of cluster synchronization via information theoretic measures. We have shown that, if the existing information measures in the literature, particularly transfer entropy, is estimated from sequential observations of continuous chaotic systems, it is hard to detect cluster synchronization, directly. On the other hand, if the state space is reconstructed from the observed data in the light of Takens’ embedding theorem first, the cluster synchronization can be detected easily.