Research Of Successive Lag Synchronization On A Class Of Generalized Complex Networks

Successive lag synchronization(SLS)is a new and important synchronization method,and it is very common in real life,such as synchronization flight of aircraft formation,the wave of people on football field,and transmission of ancient beacon fire.First of all,based on the idea of complete synchronization model,a new distributed SLS dynamic network model is established in this paper.Considering the work on the SLS in the previous research,the centralized dynamic network model is adopted to realize the complete synchronization of the network,that is to say,the global information of the network needs to be obtained to realize the SLS.Compared with the centralized network model,the distributed coupling network model between nodes has higher efficiency.In other words,the state change of each node is only related to its own dynamic behavior and the information of its neighbors,not to the global information.Then,in order to make the dynamic network realize SLS,two kinds of linear feedback controllers are designed.Among them,the distributed linear feedback controller is different from the linear feedback controller used in the previous research,which only depends on the state of the node itself.The conditions of asymptotic stability of SLS are obtained applying Lyapunov krasovski theorem,Barbarat lemma and Lyapunov function method.And the correctness of the theoretical results is verified by numerical simulation.Secondly,a kind of adaptive feedback controller is designed.And the sufficient conditions of asymptotic stability of SLS under the adaptive controller are obtained.The greater the control intensity required for the network to realize SLS means the higher control cost,so this paper designs adaptive feedback controllers.By constructing Lyapunov function,and applying the Barbarat lemma,the stability conditions of SLS are obtained.Finally,the control strength when the SLS state is achieved is less than that when the linear feedback controller is used.It means that adaptive feedback control can effectively reduce control intensity and control cost.And the correctness of the theoretical results is verified by numerical simulation.Finally,considering that the delay dependent synchronization conditions are more open than the delay independent synchronization conditions.Because for the delay dependent synchronization conditions,the system only needs to be able to achieve SLS under some delay conditions,and independent of the time delay needs to be able to achieve SLS for any large delay.That is to say,when the time delay is very small,the delay dependent conditions are loose.So the problem of delay dependent synchronization in the stability condition is studied.And the correctness of the theoretical results is verified by numerical simulation.