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 opto-electronic oscillators.
@article{arxiv.1804.01462,
title = {Symmetry- and Input-Cluster Synchronization in Networks},
author = {Abu Bakar Siddique and Louis Pecora and Joe Hart and Francesco Sorrentino},
journal= {arXiv preprint arXiv:1804.01462},
year = {2018}
}