Topology Identification Of(Fractional)Complex Dynamical Networks Based On Inter-network Synchronization

Complex networks widely exist in the real world,such as the Internet,aviation networks,social networks,transportation networks,ecosystem networks,etc.Complex networks have gradually become a frontier in interdisciplinary research,which involves mathematics,physics,biology,finance and many other subjects.As a hot research topic,a lot of achievements have been made.In the real world,network information can not be directly obtained,which is,however,usually required to be known for investigation.In order to better describe real-world networks and to reveal their inner rules,topology identification of complex networks,namely inferring the unknown topology from the known information of the network,is a topic of practical significance.In recent years,although achievements have been made,the subject is still full of challenges.The thesis mainly consists of six chapters.Chapter 1 introduces the research background of complex networks,a review for network topology identification,the outline of the thesis and the notation.Chapter 2 introduces the definition of synchronization and generalized synchronization in complex networks,fractional calculus and the stability theory of nonlinear systems.Chapters 3-5 provide the main work of the thesis.Chapter 6 summarizes the thesis and describes the future work.The main contents are as follows:Chapter 3 studies the identification of the unknown topology and system parameters in fractional-order complex dynamical networks based on the synchronization between the drive and the response network.In recent years,some research results have been obtained in the identification of fractional-order complex dynamical networks.These results come to the conclusion of successful identification according to the fact that the synchronization error between networks tends to zero with time increasing.However,this is not rigorous.The synchronization error tending to zero means that the networks achieve synchronization,which does not necessarily guarantee that the estimated values will eventually tend to the true values.In view of this,a new lemma is proposed in Chapter 3.According to the proposed lemma,the fact that the fractionalorder derivative of the error system tend to zero with time can ensure successful identification of unknown topology and parameters in the network.An example is given to illustrate that when the error system tends to zero,the fractional-order derivative of the error system may not tends to zero.In addition,numerical simulations show that the large difference in node dynamics in the network is beneficial to topology identification.Chapter 4 studies the identification of the unknown topology in fractional-order complex dynamical networks using the auxiliary system method.Most of the existing results of topology identification of fractional-order complex networks are based on synchronization between networks.In addition,there are works employing the generalized synchronization.In this chapter,based on the auxiliary system method,the unknown topology of fractional-order complex networks is identified by realizing generalized synchronization between networks.Compared with previous literature,this method does not require the drive network to contain connections between nodes,that is,the network can be composed of isolated nodes.This conclusion can provide a new idea for improving the topology identification method.Chapter 5 studies a new topology identification method based on isolated nodes excitation.The drive network consists of isolated nodes.A periodic bounded function is proposed as the drive network node dynamics.When this function satisfies some conditions,the assumption of the linear independence of the synchronization manifold commonly used in previous literature is avoided.In most of the existing literature,this linear independence assumption is indispensable for topology identification.It greatly limits the application scope of the method based on inter-network synchronization.For example,the synchronization in the network to be identified may lead to identification failure.Furthermore,this assumption currently lacks a rigorous definition and there is no clear method to verify whether the network satisfies the assumption.Compared with the existing work,the method proposed in this chapter has less strict requirements on the drive network and expands the range of identifiable networks.