Impulsive Synchroncation Of Complex Networks With Time Delay

In recent decades,the applications of complex network have been involved in many fields,such as society,biology and physics.It has become an important research topic in network science.As a universal dynamic behavior,synchronization has attracted extensive attention from researchers.Due to complexity of networks,achieving sy-nchronization is difficult only relying on inner adjust-ments of network.For achieving synchronization,it is necessary to add external controls.Based on the advantages of simple structure,low cost and easy implementation,synchronization of complex networks with time delay is investigated by introducing impulsive control scheme in this thesis.Firstly,synchronization of network with time-varying topology and delay is investigated.Proper controllers are designed for achieving synchronization by adopting impulsive control scheme.Based on linear matrix inequality technique and Lyapunov function method,a synchronization criterion about system parameters,the impulsive gains and intervals is derived.Controllers are improved by introducing adaptive strategy and an adaptive synchronization criterion is obtained correspondingly.The updating law of the impulsive gain and the method for estimating the im-pulsive instant are provided in terms of the adaptive synchronization criterion.Finally,numerical examples are performed t.o demonstrate the effectiveness of the the.oretical results.Secondly,impulsive control scheme is adopted to consider the synchronization of dynamical networks with distributed time delays.Based on the Lyapunov function method and linear matrix inequality technique,simple synchronization conditions are derived.For any given network,the impulsive intervals can be estimated from the derived conditions when the impulsive gains are fixed,and vice versa.Further,adaptive strategy is introduced t.o design unified impulsive controllers for different networks.Noticeably,in the proposed adaptive impulsive control scheme,the impulsive gains can be adjusted to needed values and the impulsive instants can be estimated adaptively.Finally,numerical examples are provided to verify the effectiveness of the theoretical results.Thirdly,community network with distributed time delays is taken into account.Cluster syn-chronization is an important dynamical behavior in community network,which denotes the nodes in the same communities have identical goals and the nodes in cdifferent communities have non-identical goals.For achieving cluster synchronization,impulsive control scheme is introduced to design proper controllers and adaptive strategy is adopted to make the impulsive controllers unified for different networks.Through taking advantage of linear matrix inequality technique and con-structing Lyapunov function,some synchronization criteria without adaptive strategy are obtained and generalized to adaptive case.Finally,numerical examples are presented to demonstrate the effectiveness of the theoretical results.Finally,we summarize the main ideas of this thesis,discuss some results about impulsive control,and put forward some issues deserving further studies.