Emergence of synchronous behavior in a network with chaotic multistable systems

Abstract

In this work, we address the synchronization problem of complex dynamical networks with bidirectional, linear, and diffusive coupling, whose nodes have dynamics given by a particular class of piecewise linear (PWL) systems. The class of PWL systems are multistable unstable dissipative systems and exhibit chaotic behavior. The topologies that we consider are regular coupled network. Firstly, we consider that the complex network has a uniform coupling strength, and through the Lyapunov approach, we show that nodes can achieve complete or partial synchronization, where the synchronization solution depends on the inner coupling matrix and the initial conditions of each node. Secondly, we consider a weighted network, where the synchronization solution depends on the external coupling matrix, and even obtain a synchronous behavior type master-slave. Our theoretical results agree with the numerical simulations for a set of nodes in different topology networks.