Synchronization of delayed complex dynamical network with hybrid-coupling via aperiodically intermittent pinning control

This paper deals with the synchronization problem of delayed complex dynamical network with hybrid-coupling, which is composed of constant coupling, discrete-delay coupling, and distributed-delay coupling. The internal time-delay of node and coupling time-delays are time-varying and can differ from each other. Based on the aperiodically intermittent control strategy, several appropriate pinning controllers and updating laws are designed in each control period. With the help of a new established differential inequality with distributed time-delay, several useful conditions to guarantee the global exponential synchronization of the complex dynamical network with mixed delays. Moreover, the minimum number of pinned nodes can be determined from the proposed criteria. Two numerical examples are provided to verify the feasibility of theoretical results.