Synchronization for nonlinearly coupled complex dynamical networks with different dimensional nodes

This paper investigates the asymptotic synchronization for the directed and undirected dynamical networks with different dimensional nodes and nonlinearly coupled functions. Besides, the nodes in the network model discussed here are dissipatively coupled and similar and their coupling coefficients between different nodes permit negative. For this kind of network model, the synchronization manifold is defined as an invariant manifold, which is regarded as the generalized case of the network with the same nodes. Furthermore, decentralized dynamical compensation controllers are synthesized to synchronize such network asymptotically based on Lyapunov stability theorem and Babalat´s lemma. Finally, numerical examples are presented to verify the effectiveness of our theoretical results.