Synchronization Of Complex Dynamical Networks Via Adaptive Impulsive Control

During last decades,the great development of information technology has made,the contact among various fields is more and more closer and the study of the networks attract more and more attention of scholars.In the study of complex networks' synchronization,impulsive control strategy,as a kind of typical discontinuous control mode,i.e.the control is exerted at certain time points,is widely used in the synchronization of networks.Based on previous research work,this paper considered three kinds of networks on the basis of impulsive control strategy:Firstly,the adaptive impulsive cluster synchronization in community networks with noniden-tical nodes is studied.In order to realize the synchronization of network,we designed the impulsive controller under the adaptive strategy.According to the Lyapunov function method,the stability analysis of impulsive differential equation and mathematical analysis technique,synchronization criteria have been derived and illustrated to be effective by several numerical simulations.Secondly,the adaptive pinning impulsive synchronization of dynamic network with time-varying delay is studied.The paper considered the synchronization of the network with time-varying coupling delay and time-varying coupling node delay.We designed the adaptive impulsive controller under the pinning strategy,and the synchronization criteria have been derived.Finally,the impulsive synchronization of time-varying dynamical network.Based on the Lyapunov function method and mathematical analysis technique.Some synchronization conditions are derived.All the derived results are illustrated to be effective by several numerical simulations.