title: Characterizing system dynamics with a weighted and directed network constructed from time series data.
abstract: In this work, we propose a novel method to transform a time series into a weighted and directed network. For a given time series, we first generate a set of segments via a sliding window, and then use a doubly symbolic scheme to characterize every windowed segment by combining absolute amplitude information with an ordinal pattern characterization. Based on this construction, a network can be directly constructed from the given time series: segments corresponding to different symbol-pairs are mapped to network nodes and the temporal succession between nodes is represented by directed links. With this conversion, dynamics underlying the time series has been encoded into the network structure. We illustrate the potential of our networks with a well-studied dynamical model as a benchmark example. Results show that network measures for characterizing global properties can detect the dynamical transitions in the underlying system. Moreover, we employ a random walk algorithm to sample loops in our networks, and find that time series with different dynamics exhibits distinct cycle structure. That is, the relative prevalence of loops with different lengths can be used to identify the underlying dynamics.
authors.affiliation: Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, People's Republic of China.
authors.forename: Xiaoran
authors.initials: X
authors.lastname: Sun
authors.affiliation: School of Mathematics and Statistics, The University of Western Australia, Crawley WA 6009, Australia.
authors.forename: Michael
authors.initials: M
authors.lastname: Small
authors.affiliation: Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, People's Republic of China.
authors.forename: Yi
authors.initials: Y
authors.lastname: Zhao
authors.affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150025, People's Republic of China.
authors.forename: Xiaoping
authors.initials: X
authors.lastname: Xue