Topology Identification Of Fractional Order Complex Networks Based On Synchronization Method

With the development of science and technology,human civilization has leaped into a century of complexity science.In recent years,research on complex networks has also become a hot spot,but most of the research on complex networks focuses on integer order models.In other words,because fractional calculus can better describe the memory and genetic characteristics of real systems,it is widely used in many fields,which makes the research of fractional calculus have new vitality.Among them,the stability theory of fractional calculus has always been a research hot topic.Therefore,this paper adopts the idea of synchronization method to identify the topology of fractional complex network has great theoretical significance and application value.This paper will take the fractional-order complex network as the research object,design the controller based on the idea of synchronization method,analyze the parameter identification mechanism theoretically,and then verify the effectiveness of the proposed method through numerical experiments.The main research work of this paper can be summarized as follows:Based on the theoretical properties of classical calculus,a response network with variable substitution control and a suitable parameter update law are constructed,and the synchronization criterion and topology identification of general fractional complex networks are studied.The results are verified.Using the theory of tempered fractional calculus and pinning control technology,sufficient conditions for partial topology recognition of tempered fractional complex networks are given by designing appropriate controllers and parameter updating laws,and a scheme to reduce the cost of local topology recognition is proposed.This method can also identify all the topologies of complex networks.Considering that the existing researches on complex networks are all continuous time type,a discrete fractional complex network model is established on the basis of continuous complex networks.By constructing the Lyapunov function and using the properties of discrete fractional calculus,synchronization criteria for discrete fractional complex networks with and without unknown topology are established based on linear matrix inequalities.