Cluster synchronization algorithms

This paper presents two approaches to achieving cluster synchronization in dynamical multi-agent systems. In contrast to the widely studied synchronization behavior, where all the coupled agents converge to the same value asymptotically, in the cluster synchronization problem studied in this paper, we require that all the interconnected agents to evolve into several clusters and each agent only to synchronize within its cluster. The first approach is to add a constant forcing to the dynamics of each agent that are determined by positive diffusive couplings; and the other is to introduce both positive and negative couplings between the agents. Some sufficient and/or necessary conditions are constructed to guarantee n-cluster synchronization behavior. Simulation results are presented to illustrate the effectiveness of the theoretical analysis.