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Chaos / Volume 22 / Issue 1 / REGULAR ARTICLES

Chaos 22, 013107 (2012); http://dx.doi.org/10.1063/1.3673789 (10 pages)

Multiscale characterization of recurrence-based phase space networks constructed from time series

Ruoxi Xiang1, Jie Zhang1,2, Xiao-Ke Xu1,3, and Michael Small1,4

1Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong, People’s Republic of China
2Centre for Computational Systems Biology, Fudan University, Shanghai 200433, People’s Republic of China
3School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520, People’s Republic of China
4School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia

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(Received 9 June 2011; accepted 12 December 2011; published online 17 January 2012)

Recently, a framework for analyzing time series by constructing an associated complex network has attracted significant research interest. One of the advantages of the complex network method for studying time series is that complex network theory provides a tool to describe either important nodes, or structures that exist in the networks, at different topological scale. This can then provide distinct information for time series of different dynamical systems. In this paper, we systematically investigate the recurrence-based phase space network of order k that has previously been used to specify different types of dynamics in terms of the motif ranking from a different perspective. Globally, we find that the network size scales with different scale exponents and the degree distribution follows a quasi-symmetric bell shape around the value of 2k with different values of degree variance from periodic to chaotic Rössler systems. Local network properties such as the vertex degree, the clustering coefficients and betweenness centrality are found to be sensitive to the local stability of the orbits and hence contain complementary information.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. QUANTITATIVE ASSESSMENT OF RECURRENCE-BASED PHASE SPACE NETWORKS
    1. Global network characteristics
      1. Average path length
      2. Clustering coefficient
      3. Degree distribution
    2. Local network characteristics
      1. Local vertex degree
      2. Clustering coefficient of a specific vertex
      3. Betweenness centrality of a specific vertex
  3. EFFECT OF NOISE
  4. ANALYSIS OF TIME SERIES FROM CLARINET DATA
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

complex networks, time series

PACS

  • 89.75.Hc

    Networks and genealogical trees

  • 05.45.Tp

    Time series analysis

  • 02.50.-r

    Probability theory, stochastic processes, and statistics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3673789

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, and J. Kurths, Phys. Rev. E 81, 015101 (2010).

    Y. Zou, R. V. Donner, J. F. Donges, N. Marwan, and J. Kurths, Chaos 20, 043130 (2010)CHAOEH000020000004043130000001.

    E. Estrada and J. Rodríguez-Velázquez, Phys. Rev. E 71, 056103 (2005).

    H.-J. Kim and J. M. Kim, Phys. Rev. E 72, 036109 (2005).

    M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002).

    M. E. J. Newman and M. Girvan, Phys. Rev. E 69, 026113 (2004).

    M. Small, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 87, 188101 (2001).


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