Finite‐time cluster synchronization of heterogeneous complex dynamical networks with discontinuous interactions

Abstract

Abstract In this paper, finite‐time cluster synchronization (FTCS) in networks of nonidentical coupled dynamical systems is addressed by introducing a discontinuous interaction rule. This interaction rule overcomes the effect of heterogeneous dynamics among nodes. It is proven that with proper coupling gain, the dynamics of the coupled system converges into the kernal space of the graph Laplacian matrix in finite time. Then sufficient conditions for FTCS are provided. In addition, the discontinuous interactions rule is applied to investigate finite‐time intra‐layer synchronization in multiplex networks.

Keywords

• distributed control
• nonlinear control systems
• synchronisation