Research On Synchronization Control For Multi-layer Complex Networks

With the development of information technology,the theoretical research and application of complex networks have gone deep into many fields.It can solve many practical system problems including the World Wide Web,the social network,the neural network and the power system network.At present,the research of networks has become one of the hot topics in network science and other fields.In practice,the multi-layer networks can better reflect the characteristics of complex dynamical systems.Multiple control strategies of controlling the synchronization of multi-layer networks need to be further popularized.On the basis of existing research results,this thesis introduces several kinds of control strategies to control of two-layer networks,from which to achieve synchronization.The first part is based on the coupling relationship between two-layer networks,we design an aperiodic intermittent control strategy.This thesis discusses two-layer network synchronization issues between the layers and obtains the sufficient conditions for networks to achieve synchronization between the layers by constructing Lyapunov function,the result is the development of the existing synchronization between the two-layer networks,the accuracy of the numerical simulation result is verified.In the second part,the inter-layer synchronization problem of a two-layer networks with time delay is studied.For this model,two different hybrid control strategies: hybrid impulse control and hybrid adaptive control,are proposed.By constructing the Lyapunov function and using the inequality techniques,the synchronization criteria of the two-layer networks with time-delayed dynamic nodes are obtained.The result is new and improves inter-layer synchronization of existing two-layer networks and reduces control costs.In the third part,the problem of inter-layer generalized synchronization is considered on the time scale.In order to realize inter-layer generalized synchronization of the two-layer networks,a dynamic event trigger control strategy is designed.Based on the time scale theories,Lyapunov methods and the inequality techniques,the synchronization criteria of two-layer networks on time scale are established.In this part,the generalized synchronization problem of two-layer networks is studied under more general conditions.The results obtained are new and improve the existing inter-layer synchronization of two-layer networks.In addition,static and dynamic event triggering conditions are compared,and the avoidance of Zeno behavior is discussed.Finally,a numerical example is given to verify the accuracy of the theoretical results.