Combinatorial synchronization of complex multiple networks with unknown parameters

In this paper, a combinatorial inner synchronization within a sub-network, which consists of four-wing chaotic system with unknown parameters and external disturbances as node dynamics, and a combinatorial outer synchronization between different sub-networks are investigated. Based on the Lyapunov stability theory, LaSalle's invariance principle, cluster analysis, and pinning control technique, some sufficient conditions, which can ensure not only the combinatorial inner synchronization of the nodes with identical node dynamics in a sub-network, but also the combinatorial outer synchronization of the sink nodes with identical or nonidentical ones between different sub-networks by a suitable switch control scheme, are obtained. By using the pinning control, only the sink node within a sub-network which has direct connections to the sink nodes in other sub-networks needs to be controlled. Finally, some numerical simulations are presented to demonstrate the feasibility and validity of the obtained results by taking the star-like topological structure as an example.