Research And Application Of Cootrollability With Complex Networks

Studying various complex systems from the perspective of complex networks can better predict the overall behavior of the system and become an important topic of complexity science since the 21st century.The ultimate goal of its research is to control the network and better serve humanity.However,the current research on the controllability of complex networks is only based on the controllability method in the linear system theory.It is qualitatively judged whether the network is controllable,but cannot know the size of network controllability.Therefore,in this thesis,we propose an index to quantitatively measure the controllability of any given network,and uses classical model networks,power networks,and metabolic networks to verify and conduct controllability research.Based on control center and the conditions number with the characteristics of nonsingularity of matrix,an index for quantitative measurement of the controllability is proposed for arbitrary networks.In the further study,the controllable decomposition is introduced to improve the index,so as to achieve quantitative measurement of the controllability of the incompletely controllable network.Then it is applied to three classical network models to analyze the influence of network topology parameters on controllability,and verify the effectiveness of the proposed index in the controllability analysis of classical network models.The power network is analyzed by the quantitative controllability index proposed in this thesis.IEEE118 power test network,Northeast power network,UHV grid network are selected as research objects to build topology model.According to the obtained network model,the differences of topological features between these networks and classical network models with the same scale and the same parameters are analyzed,and the relationship between these network topologies and network controllability is further analyzed.From the simulation results,it is found that most power networks have smaller average path lengths and higher clustering coefficients,which belong to small world networks;and the smaller the average degree,the greater the heterogeneity,the lower the controllability of the network;the sparse and heterogeneous power networks are more difficult to control than models of the same size.Metabolic networks are also analyzed using the proposed controllability index.Firstly,topological modeling is carried out for the selected E.coli transcription network,yeast metabolic network and protein structure networks with different nodes.Then,according to the obtained metabolic network model,we generate corresponding classical network models and CM configuration model network with the same degree distribution as metabolic networks,and topology characteristics and controllability analysis are performed on various networks.Ac cording to the simulation results,the controllability of the metabolic network is not only related to the degree distribution,but also related to the heterogeneity;and the greater the ratio of heterogeneity to the average degree,the lower the controllability of the network;the sparse heterogeneity metabolic networks are more difficult to control than model networks of the same size.