Study On Synchronization Control Of Fractional Complex-Variable Complex Network

Complex network is a new subject in complexity science.It can describe complex model of social science,natural science and engineering technology very well.It takes physics,mathematics and computer as the research tools,and takes complex system as the research target.Fractional order differential equation to describe the dynamical features of the nonlinear system has more advantages than the integer order,a fractional order complex networks can better describe the model with memory and genetic properties,on the other hand,the fractional order complex networks through the fractional derivative adds a degree of freedom,has greatly enriched the dynamic behavior.In recent years,people have extended complex networks to the field of complex numbers.The complex variable dynamic network can be regarded as an extension of the real variable dynamic network,which doubles the number of variables,thus improving the security of information transmission.Therefore,the synchronous control of complex networks with fractional complex variables has a wider application space.Based on Lyapunov stability theorem,linear matrix inequalities,nonlinear fractional stability theory and LaSalle invariance principle,we discuss and analyze synchronization control of complex networks with fractional order complex variables.By controlling the nodes in the network,the complex network is synchronized.At the same time,the judgment standard of network synchronization is obtained.Finally,the accuracy of the theory is verified by experimental simulation,and the design controller is proved to be reasonable.The main contents and innovations of this thesis are as follows:(1)In the previous discussion,researchers often only consider the analysis of real-domain dynamic networks.In this paper,based on the fractional calculus theory,the synchronization results of complex networks in complex fields are considered,and the rationality of the theoretical results is verified by simulation.(2)Because the network contains many nodes,it is not practical to add a controller to all network nodes to drive it to synchronize.Therefore,the researchers proposed pinning control method.In this paper,the pinning pattern based on tight centrality is used to select the corresponding pinning nodes.The nodes of the network are considered as complex-variable Lorenz chaotic systems and complex-variable Chen chaotic systems,and their numerical simulations are carried out.The experimental results show that the proposed control mechanism is effective and can guarantee the synchronization of the whole network.(3)As adaptive feedback control itself can change the control coefficient accordingly,it is widely used in the field of control.Combined with the characteristics of adaptive control method and the advantage of pinning mode,the synchronization control of complex networks with fractional order complex domain is effectively carried out.At the same time,the structure of fractional complex variable network based on time-varying coupling is given,and its synchronization is analyzed.