Cluster synchronization in the adaptive complex dynamical networks via a novel approach

This Letter investigates cluster synchronization in the adaptive complex dynamical networks with nonidentical nodes by a local control method and a novel adaptive strategy for the coupling strengths of the networks. In this approach, the coupling strength of each node adjusts adaptively only based on the state information of its neighborhood. By means of the proposed scheme, the sufficient conditions for achieving cluster synchronization are derived analytically by utilizing Lyapunov stability theory. It is demonstrated that the synchronization performance is sensitively affected by the control gain, the inner-coupling matrix and the network topological structure. The numerical simulations are performed to verify the effectiveness of the theoretical results.

► We present a more realistic adaptive complex network model with diverse nodes.
► The local controllers are designed based the community structure of the network.
► Each nodeʼs coupling strength adapts self only by the state of its neighborhood.
► The synchronization effect is affected by the network structure and control gain.
► The Cluster synchronization method is robust against noise perturbation.