Lag Synchronization Of Complex Networks With Multi-derivative Coupling And Multi-output Coupling

More recently,an enormous research interest has been devoted to the dynamical behaviors of complex networks(CNs),especially synchronization,and lots of meaningful results have been obtained.Unfortunately,in the most existing works,a huge number of authors only consider the synchronization problem for state coupled CNs.As the matter of fact,there exist three kinds of coupling forms in the CNs: state coupling,output coupling,derivative coupling.Consequently,it is worthwhile discussing synchronization of CNs with derivative coupling or output coupling.On the other side,comparing with traditional network model,the real-life networks should be depicted as the CNs with multi-weights,such as social networks,coupled neural networks,etc.Therefore,it makes the synchronization for CNs with multiple derivative couplings and multiple output couplings is worthy of being studied further.Moreover,the time-delay commonly exists due to the finite speed of transmission and network congestion,which is always considered as the impact factor for the instability of system.Therefore,it is very intriguing to research the lag synchronization for the CNs.Furthermore,in the real-life world,there may exist the external disturbances(EDs)in CNs.As the matter of fact,the synchronization in CNs may be destroyed on account of the existence of EDs.Consequently,the lag H_?!synchronization problem for CNs is worthy of being studied further.Moreover,in some cases,it is difficult to measure and observe the state of node in CNs.Therefore,it is very meaningful to consider the lag output synchronization of CNs.But,the lag synchronization and lag H_?! synchronization for CNs with multiple derivative couplings,and lag output synchronization of CNs with multiple output couplings have not been discussed.This paper mainly devotes to studying the lag synchronization problem of CNs with multiple derivative couplings and multiple output couplings.The lag synchronization and lag H_?! synchronization for CNs with multiple derivative couplings are respectively taken into consideration in the chapter II.On one side,by virtue of devising state feedback controller and adaptive feedback controller,two lagH_?! synchronization criteria for CNs with multiple derivative couplings are established.On the other side,based on selecting state feedback controller and adaptive state feedback controller,the lag synchronization of multiple derivative coupled CNs is also discussed.In the chapter III,the lag output synchronization problem of multiple output coupled CNs with positive semidefinite or positive definite output matrix is addressed.We not only employ output feedback control strategy and adaptive output feedback control strategy to consider the lag output synchronization of multiple output coupled CNs with positive definite output matrix,but also utilize the similar approaches to study the lag output synchronization for network model with positive semidefinite output matrix.Finally,several numerical examples are put forward to verify the lag synchronization,lag H_?!synchronization and lag output synchronization criteria.