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Related Experiment Videos

Master equation approach to synchronization in diffusion-coupled nonlinear oscillators

Vance1, Ross

  • 1Department of Chemistry, Stanford University, Stanford, California 94305, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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Internal fluctuations impact phase synchronization in oscillatory systems. In higher dimensions (d≥3), synchronized states can exist, while lower dimensions (d<3) exhibit rough states where phase fluctuations increase with system size.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Oscillatory reaction-diffusion systems are fundamental in various scientific fields.
  • Understanding the role of internal fluctuations is crucial for predicting system behavior.
  • Phase synchronization is a key phenomenon in coupled oscillatory systems.

Purpose of the Study:

  • To investigate the influence of internal fluctuations on phase synchronization.
  • To analyze the behavior of oscillatory reaction-diffusion systems in the large system size limit.
  • To determine the conditions for stable phase synchronization in different spatial dimensions.

Main Methods:

  • Master equation approach to model internal fluctuations.
  • Eikonal approximation for analyzing probability density in large systems.

Related Experiment Videos

  • Reduction to Hamilton-Jacobi and nonlinear diffusion equations.
  • Equivalence established between diffusion-coupled oscillators and the Kardar-Parisi-Zhang (KPZ) equation.

    • Main Results:

    • For 1D systems, phase width diverges as w ~ L^(1/2), indicating rough phase locking.
    • Spatially synchronized states are predicted to exist only in dimensions d≥3.
    • In dimensions d=1 and d=2, a rough state emerges with algebraically diverging phase width (α>0).

    Conclusions:

    • Internal fluctuations significantly affect phase synchronization, leading to different states based on dimensionality.
    • The study provides a theoretical framework connecting reaction-diffusion systems with surface growth phenomena (KPZ equation).
    • Synchronization is robust in higher dimensions but susceptible to roughness in lower dimensions.