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Chaos / Volume 21 / Issue 4 / REGULAR ARTICLES

Chaos 21, 043129 (2011); http://dx.doi.org/10.1063/1.3664396 (9 pages)

Detecting the topologies of complex networks with stochastic perturbations

Xiaoqun Wu1, Changsong Zhou2, Guanrong Chen3, and Jun-an Lu1

1School of Mathematics and Statistics, Wuhan University, Hubei 430072, China
2Department of Physics, Center for Nonlinear Studies, Hong Kong Baptist University, Hong Kong
3Department of Electronic Engineering, City University of Hong Kong, Hong Kong

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(Received 6 June 2011; accepted 8 November 2011; published online 2 December 2011)

How to recover the underlying connection topology of a complex network from observed time series of a component variable of each node subject to random perturbations is studied. A new technique termed Piecewise Granger Causality is proposed. The validity of the new approach is illustrated with two FitzHugh-Nagumo neurobiological networks by only observing the membrane potential of each neuron, where the neurons are coupled linearly and nonlinearly, respectively. Comparison with the traditional Granger causality test is performed, and it is found that the new approach outperforms the traditional one. The impact of the network coupling strength and the noise intensity, as well as the data length of each partition of the time series, is further analyzed in detail. Finally, an application to a network composed of coupled chaotic Rössler systems is provided for further validation of the new method.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORY
    1. Granger causality
    2. Conditional Granger causality
    3. Piecewise Granger causality
  3. NUMERICAL SIMULATIONS
    1. Networks of neural systems
    2. Network of chaotic oscillators
  4. CONCLUSION

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KEYWORDS and PACS

Keywords

complex networks, perturbation theory, random processes, stochastic processes, time series, topology

PACS

  • 89.75.Hc

    Networks and genealogical trees

  • 05.40.-a

    Fluctuation phenomena, random processes, noise, and Brownian motion

  • 02.40.Pc

    General topology

  • 02.50.-r

    Probability theory, stochastic processes, and statistics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3664396

PUBLICATION DATA

ISSN

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

Publisher

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

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