Fixed-time cluster synchronization in directed community networks with diverse coupling and different-order nodes

摘要

In this paper, fixed-time cluster synchronization of directed community networks (DCNs) with diverse coupling and different-order nodes is explored. For the DCN model, the inherent dynamics and state dimensions of the nodes in different communities can be nonidentical, and moreover, the interactive nodes can differ in their types of connections in different communities and the connections between any pair of different communities can be nonidentical as well. Two types of control strategies, state feedback control and adaptive feedback control, are adopted to force such DCNs to realize cluster synchronization in fixed-time. By utilizing reduction to absurdity, some sufficient conditions ensuring the fixed-time cluster synchronization are derived for the proposed two control schemes. Moreover, it is revealed theoretically that our estimated settling time is more precise and less conservative than that presented in the previous researches. Finally, the validity of the obtained fixed-time cluster synchronization criteria is verified via numerical simulations.