Pinning outer synchronization between two delayed complex networks with nonlinear coupling via adaptive periodically intermittent control

This paper is concerned with the problem of pinning outer synchronization between two delayed complex networks with nonlinear coupling. Both the internal delay and coupling delay are included in coupled network model. By designing appropriate adaptive intermittent controllers and using the Lyapunov stability theory, some pinning outer synchronization criteria are derived, which can guarantee the response network asymptotically synchronizes to drive network. Furthermore, the restrictions about delay and control width are removed. Simultaneously, two simple adaptive intermittent pinning outer synchronization conditions are obtained based on the proposed criteria. A numerical example is provided to demonstrate the effectiveness of the theoretical results.