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Collective phase sensitivity.

Yoji Kawamura1, Hiroya Nakao, Kensuke Arai

  • 1The Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan.

Physical Review Letters
|September 4, 2008
PubMed
Summary

This study formulates the collective phase response for globally coupled oscillators. It quantifies the stability of common-noise-induced synchronization in oscillator populations.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Complex systems

Background:

  • Understanding collective behavior in systems of interacting nonlinear oscillators is crucial for various scientific fields.
  • Macroscopic phase response quantifies how an oscillator population's collective rhythm is affected by external influences.
  • Previous methods often lacked a detailed link between microscopic oscillator behavior and macroscopic population dynamics.

Purpose of the Study:

  • To develop a general method for calculating the collective phase response of globally coupled nonlinear oscillators.
  • To apply this method to analyze the stability of synchronization induced by common noise in uncoupled oscillator populations.
  • To bridge the gap between microscopic phase sensitivity and macroscopic phase response.

Main Methods:

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  • Formulation of collective phase response for globally coupled oscillators.
  • A two-step phase reduction technique to derive macroscopic phase sensitivity from microscopic properties.
  • Application of the derived sensitivity to analyze noise-induced synchronization stability.

Main Results:

  • A precise formulation for the collective phase response of globally coupled nonlinear oscillators.
  • The macroscopic phase sensitivity was successfully derived from microscopic phase sensitivity.
  • The stability of common-noise-induced synchronization in two uncoupled oscillator populations was quantified.

Conclusions:

  • The developed phase reduction method provides a powerful tool for analyzing complex oscillator populations.
  • The study offers insights into the mechanisms and stability of noise-induced synchronization.
  • This work contributes to the understanding of collective phenomena in physical and biological systems.