Dual Characterization Between Network Structure And Time Series With Its Application

As a current focus of research,complex science has two typical paradigms: time series and complex network.Due to limitations of the single paradigm,it is important to construct the equivalent mapping between the two paradigms.Meanwhile,the classical structural features in network mainly include small world phenomenon,heterogeneous phenomenon and network community phenomenon.In consideration of the structural features in network,based on the mapping between the two paradigms,qualitative and quantitative analysis between the network structural features and the time series which implement the application between the two paradigms.In this article,first improved the finite memory random walk.Then qualitative analysis of the structural features in network based on time series with the multiscale entropy method.Furthermore,study on the characterization and application of network community structure based on time series.In the end,on the basis of the novel and equivalent mapping,this article presses on the association between the community phenomena in network and the dynamics of time series.In the light of basic structural features in network,such as small world and heterogeneous,this article focuses on the characterization and application in time series.Specifically,take the spectral analysis into account,the article proposes the improved method which based on the finite memory random walk to transform network to time series.With applied to the classical network models,the multiscale entropy method based on the time series is for describing qualitatively the basic structural features in network.Meanwhile the multiscale entropy method is also applied to some nonlinear dynamical systems.The similarity of the trend will be found between the nonlinear dynamical systems and the corresponding time series constructed by network,which provides groundwork of characterization and application about the structural features in network by time series.Considering the network community structure,this article presents a new community detection algorithm based on time series.The k-means algorithm finds out the best clusters of the time series transformed from some benchmark networks,which are the community composition of benchmark networks.The experimental results show that the range distribution of time series is obviously different with different communities in network.At the same time,the community detection algorithm based on time series has good performance in artificial network,karate network and other realistic benchmark networks.It shows that characterization and application in network community structure based on the time series.Furthermore,the analysis on the association relationships between the network community structure and the dynamics of time series.This article proposes a novel map which can transform the time series into the undirected and weighted network and presents the theoretical foundation of equivalence about the mapping.Apply a classical algorithm for detecting community structure in network constructed by an ensemble of time series ranging from periodic to chaotic.Emphasis here is on capturing deterministic dynamical information with community structure directly.The results suggest that there are strong associations between the network community structure and the dynamics in time series.The characterization and application between time series and network structural features are further improved.