Research On Structural Controllability Of General Edge Dynamics In Complex Network

Complex network is a complex system abstracted from a large number of individuals and their interactions,covering mathematics,statistics,cybernetics,physics and other disciplines.In recent years,people have become increasingly interested in the structural characteristics and dynamic behavior of complex networks,and how to control a network has become a focus of research.The current research on complex network control mainly focuses on the nodal dynamic systems of networks,where the system states correspond to the nodes in the network,and the coupling relationship between states corresponds to the edges between nodes.The edge dynamic system of the network corresponds to the nodal dynamic system,where the edges correspond to the states in the system,and the switching matrix in the nodes describes the interaction relationship between the in-and out-edges states of the nodes.The research on complex network edge dynamic systems provides people with new concepts and ideas.In this thesis,the structural controllability and related problems of complex network edge dynamic system are studied.The research contents are as follows:The general structural controllability of complex network edge dynamic systems is studied.In the traditional study of controllability of edge dynamic systems,it is assumed that the states of all adjacent edges are coupled.This article removes the all-to-all coupling constraint and proposes a generalized edge dynamic system model that allows for fixed zero parameters and independent free parameters in the exchange matrix of nodes.We studied the theoretical framework for the generalized structural controllability of edge dynamic systems and found that the set of driving nodes for the controllability of edge dynamic systems is unique and determined by the local information of the nodes.Applying the theoretical framework to a large number of models and real networks,it is found that there are upper and lower bounds on the controllability of edge dynamic systems,which are determined by the proportion of adjacent edge state coupling.The influence of coupling on the generalized structural controllability of edge dynamic systems are studied.Based on the real network analysis,it is found that most of the coupling is not involved in the control of edge dynamic systems.Therefore,we proposed a quantitative method of numerical integration based on effective coupling.Based on the analysis of model network and real network,it is found that homogeneous networks and relatively sparse networks contain high effective couplings in numerical integration.It is found that effective coupling numerical integration is positively correlated with degree correlation,and effective coupling numerical integration is determined by degree distribution.The role of edges in the general structural controllability of edge dynamic systems has been researched.Based on edge classification,the role of edges in the controllability of edge dynamic systems is quantified,and a method for judging edge classification based on node local information is proposed.Based on the analysis of real network and model network,it is found that the proportion of three sides is largely determined by coupling density and degree distribution,and is affected by degree correlation.When the coupling density is large enough,dense and homogeneous networks have lower proportions of critical edges,replaced by ordinary and intermittent edges.