Research On Pinning Control Methods Of Complex Networks Based On Important Nodes

Because synchronization can explain many physical phenomena and its many potential applications,it is studied by many scientists in the last years.In most cases,complex networks cannot achieve synchronization by themselves,so the effective control methods are required to make the complex networks achieve synchronization.Among the many control methods,pinning control method has a great advantage on the large-scale network.However,the method should be further studied.Base on the previous research,this paper makes an deep study on the pinning control method based on important nodes.The main research work is as follows:(1)Use pinning control method to achieve more general complex networks’ synchronization.First,a complex network model with a node time delay term,a node without time delay term,a coupling time delay term,a coupling without time delay term and external interference term is proposed.Moreover,the coupling time delay term’ coupling strength can be different with the non-time delay coupling term’s.The coupling matrix and the inner coupling matrix also can be different.In this paper,the pinning control method is used to achieve synchronization,the sufficient conditions are also given.(2)Then this paper also investigate the unbounded double time delay problem and make the complex network with unbounded double time delay achieve μ-stability via pinning control method.The node delay and the coupling delay can be different in this paper.To make the complex network model more close to the real network model,the fixed coupling strength is used.The sufficient conditions are given.(3)New pinning control methods are proposed in this paper.Point at undirected unweighted complex network,the DF(Data flow)-based pinning control method has been proposed.The method’s effective has been proved,the sufficient conditions are given and this method has been compared with the proposed methods.(4)Point at directed weighted complex network,4 pinning control method are proposed in this paper.Pinning control method’s effective has been proved theoretical and the sufficient conditions are given.This paper also compare the 4 pinning control methods based on 3different index which can evaluate synchronization performance.