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Chaos / Volume 22 / Issue 1 / REGULAR ARTICLES

Chaos 22, 013115 (2012); http://dx.doi.org/10.1063/1.3677367 (12 pages)

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Yong Zou1,2,3, Reik V. Donner1, and Jürgen Kurths1,4,5

1Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany
2Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
3Department of Physics, East China Normal University, 200062 Shanghai, China
4Department of Physics, Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany
5Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB 24 UE, United Kingdom

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(Received 20 October 2011; accepted 27 December 2011; published online 2 February 2012)

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. METHODS
    1. Recurrence time statistics
    2. Recurrence network analysis
    3. Recurrence properties of phase-coherent and noncoherent Rössler systems
  3. QUANTIFYING PHASE COHERENCE OF CHAOTIC OSCILLATORS
    1. Phase and frequency of chaotic oscillators
    2. Traditional measures of phase coherence
    3. RP-based indicators of phase coherence
  4. EXAMPLE I: BIFURCATION SCENARIO OF THE RÖSSLER SYSTEM
    1. Traditional and recurrence times-based measures
    2. Recurrence network measures
    3. Discriminatory skills of RP-based phase coherence indicators
    4. Impact of the homoclinic point on RN measures
  5. EXAMPLE II: BIFURCATION SCENARIO OF THE MACKEY-GLASS SYSTEM
  6. CONCLUSIONS

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KEYWORDS and PACS

Keywords

chaos, geometry, nonlinear dynamical systems, numerical analysis, time series

PACS

  • 05.45.Tp

    Time series analysis

  • 02.50.-r

    Probability theory, stochastic processes, and statistics

  • 02.60.-x

    Numerical approximation and analysis

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3677367

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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