Symmetry- and input-cluster synchronization in networks

Abstract

We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital partitions of the network nodes (symmetry-cluster synchronization) and equitable partitions of the network nodes (input-cluster synchronization). Our results are verified experimentally in networks of coupled optoelectronic oscillators.