Numerical studies on the synchronization of a network of mutually coupled simple chaotic systems

Abstract

We present in this paper, the synchronization dynamics observed in a network of mutually coupled simple chaotic systems. The network consisting of chaotic systems arranged in a square matrix network is studied for their different types of synchronization behavior. The chaotic attractors of the simple $2 \times 2$ matrix network exhibiting strange non-chaotic attractors in their synchronization dynamics for smaller values of the coupling strength is reported. Further, the existence of islands of unsynchronized and synchronized states of strange non-chaotic attractors for smaller values of coupling strength is observed. The process of complete synchronization observed in the network with all the systems exhibiting strange non-chaotic behavior is reported. The variation of the slope of the singular continuous spectra as a function of the coupling strength confirming the strange non-chaotic state of each of the system in the network is presented. The stability of complete synchronization observed in the network is studied using the Master Stability Function.