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Detecting local synchronization in coupled chaotic systems.

L Pastur1, S Boccaletti, P L Ramazza

  • 1Istituto Nazionale di Ottica Applicata, Largo Enrico Fermi 6, 50125 Florence, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2004
PubMed
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We developed a new technique to detect local dependencies in chaotic systems, even without global synchronization. This method quantifies how often local predictions are possible within coupled chaotic signals.

Area of Science:

  • Nonlinear dynamics
  • Complex systems analysis
  • Chaos theory

Background:

  • Coupled chaotic systems exhibit complex behaviors.
  • Global synchronization is a common measure, but local interactions can exist independently.
  • Understanding local functional dependencies is crucial for analyzing complex systems.

Purpose of the Study:

  • To introduce a novel technique for detecting and quantifying local functional dependencies in coupled chaotic systems.
  • To assess the fraction of locally synchronized configurations irrespective of global synchronization.
  • To apply the method to interacting Rössler oscillators.

Main Methods:

  • Development of a technique to estimate the fraction of locally synchronized configurations.
  • Analysis of pairs of signals with arbitrary states of global synchronization.

Related Experiment Videos

  • Application to a system of interacting Rössler oscillators.

    • Main Results:

    • The method successfully detects and quantifies local functional dependencies.
    • It can identify dynamical configurations enabling local prediction tasks.
    • Quantification is possible even when global synchronization features are absent.

    Conclusions:

    • The introduced technique effectively quantifies local functional dependencies in coupled chaotic systems.
    • It provides insights into system dynamics beyond global synchronization measures.
    • This method enhances the analysis of complex interactions in chaotic systems.