Controllability Of Complex Network Based On Network Core

With the wide application of complex networks in the fields of information,medicine and transportation,more and more researchers have devoted themselves to the study and analysis of complex network dynamics.One of the most important research fields is the control of complex networks,which makes the complex networks develop in the desired direction.Based on the controllability theory of complex networks,the core-based complex network the practical control problem is studied in this paper.Firstly,the sufficient and necessary condition of the control of complex networks based on core is analyzed through PBH control condition.And then an effective method of setting control input matrix to control the networks is proposed.The method shows that under certain conditions,the whole network can be controlled by controlling the core of the network.The result of theoretical analysis is verified by an example,which shows the correctness and feasibility of the theory.Secondly,to solve the problem that the core is controllable but the network itself is not controllable,some solutions are proposed by using controllable conditions of PBH.Two controllable solutions of replacing the driver node group and adding driver nodes are proposed.The example shows the correctness and feasibility of the method.Finally,extending to general situation,it is proved that increasing the control of the one-degree in the process of each leaf deletion,the entire network is controllable.In particular,for network composed of core and path,a simple and effective control method is proposed,and an example is used to illustrate the feasibility of the method.