Exponential synchronisation of united complex dynamical networks with multi-links via adaptive periodically intermittent control

Based on a method of network split according to the different nature of time-delay, the model of the united directed complex networks with multi-links are established. The exponential synchronisation of this model via adaptive periodically intermittent control is further investigated in this study. Via the Lyapunov stability theory combined with the method of the adaptive control, pinning control and periodically intermittent control, some novel and simple criteria are derived for the global exponential synchronisation of the complex dynamical networks with multi-links, and the derived results are less conservative. Several corresponding adaptive feedback synchronisation controllers, pinning controllers and impulsive controllers are designed, respectively. The restriction on the control width and the time delay are removed. This leads to a larger application scope for this method. Using chaotic system as the nodes of the networks, some numerical examples of the united directed complex networks with multi-links and delayed complex networks are given to demonstrate the effectiveness of the control strategies, respectively.