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General framework for phase synchronization through localized sets.

T Pereira1, M S Baptista, J Kurths

  • 1Nonlinear Dynamics, Institute of Physics, University of Potsdam, D-14415, Potsdam, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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We developed a new method to detect phase synchronization in chaotic oscillators without measuring phase directly. This approach helps identify synchronized clusters and understand information exchange in coupled systems.

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Phase synchronization (PS) is crucial for information exchange in coupled chaotic oscillators.
  • Identifying PS typically requires direct phase measurement, which is often impractical.
  • Coupled chaotic systems, like neuronal networks, exhibit complex dynamics.

Purpose of the Study:

  • To introduce a novel, phase-measurement-free approach for identifying phase synchronization.
  • To demonstrate the method's applicability to oscillators with multiple time scales.
  • To explore the relationship between localized sets, emergent synchronization, and information exchange.

Main Methods:

  • Defining a 'typical event' in one oscillator to trigger observations in others.

Related Experiment Videos

  • Analyzing the resulting localized sets to infer phase synchronization.
  • Applying the method to networks of chemically coupled neurons.

    • Main Results:

    • The approach successfully identifies phase synchronization without explicit phase measurement.
    • Localized sets reveal emergent clusters of phase-synchronous neurons prior to global synchronization.
    • A correlation is established between localized sets and the capacity for information exchange.

    Conclusions:

    • The presented method offers a general and accessible tool for detecting phase synchronization in complex systems.
    • Early emergence of phase-synchronous clusters facilitates information exchange in neuronal networks.
    • The localized set analysis provides insights into information transfer mechanisms in coupled chaotic oscillators.