Synchronization And Topology Identification Of Multiplex Delayed Network

In recent years,the research of complex networks has penetrated into many different fields,such as mathematical science,engineering and life science.Although the study on complex networks has experienced rapid development in the past few years,many realworld networks cannot be easily abstracted by monoplex ones with the development of network science.The study on multiplex networks is becoming one of the most advanced and important branches of network science very recently.Different from these multiplex networks,the thesis focuses on synchronization and topology identification of multiplex network with multiple time delays.The thesis consists of six chapters.In Chapter 1,we will introduce some fundamental knowledge of complex networks.In Chapter 2,we briefly introduce some preliminary knowledge relevant to the remainder parts.Then,the main results and ideas of our work will be given in Chapters 3-5.Besides,we introduce the model of multiplex network with multiple time delays.In Chapter 6,the main contents of this thesis and some outlook for further research work are discussed.The main contents and innovations are summarized as follows.1)Synchronization is one of the most important topics in complex networks.At present,the researches on synchronization of multiplex networks are mainly focused on two topics: the network parameters to impact the synchronization ability,and design the control schemes to achieve the synchronization.Including inter-layer synchronization,intra-layer synchronization,and complete synchronization,etc..Due to the complexity of multiplex networks,pinning mechanism is expected to be particularly effective.However,noise exists everywhere because of the environmental disturbances or uncertainties.Meanwhile,noise is also a “double-edged sword”.How to make good use of noise is a problem to be solved.Therefore,the research on the noise system has also attracted extensive attention.Based on the LaSalle-type invariance principle for stochastic differential delay equations and Lyapunov stability theory,it is concluded that the simple adaptive feedback control and pinning adaptive feedback control are valid for the multiplex networks with multiple delays and noises.In addition,we further discuss the impact of the difference of noise perturbations,time delays,and coupling strengths among each layer on the number of pinned nodes.We find that the number of pinned nodes increases with the interval of noise and the interval of time delay,decreases with the interval of intra-layer coupling strength.2)In practical situations,the exact topology of a network is usually unknown or uncertain,thus the necessity of identifying the topology arises.In the past few years,topology identification has made great progress.The synchronization-based estimation theory is one of the most important methods for topology identification.The thesis discusses the identification of the topology and unknown parameters of the multiplex delayed networks with stochastic noises and output variables,respectively.Moreover,the master stability function method is used to discuss the impact of two network parameters on the identification performance.Numerical results show that the inner coupling matrices and time delays have significant impact on topology identification.With the fixed inner couplings(time delay)of one layer,the logarithmic growth of other layer's inner couplings(time delay)in a certain range is beneficial to the identification performance.