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Phase reduction method for strongly perturbed limit cycle oscillators.

Wataru Kurebayashi1, Sho Shirasaka, Hiroya Nakao

  • 1Graduate School of Information Science and Engineering, Tokyo Institute of Technology, O-okayama 2-12-1, Meguro, Tokyo 152-8552, Japan.

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This study introduces a generalized phase reduction method for analyzing strongly perturbed limit cycle oscillators. The new method accurately predicts synchronization dynamics, overcoming limitations of conventional approaches for complex rhythmic phenomena.

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Area of Science:

  • Theoretical physics
  • Nonlinear dynamics
  • Complex systems

Background:

  • The conventional phase reduction method is effective for weakly perturbed limit cycle oscillators.
  • Rhythmic phenomena are crucial in various scientific fields, including biology and physics.
  • Analyzing strongly perturbed oscillators remains a challenge for existing theoretical frameworks.

Purpose of the Study:

  • To develop a generalized phase reduction method applicable to limit cycle oscillators under strong perturbations.
  • To enable the analysis of rhythmic phenomena with significant variations in oscillation shape and frequency.
  • To accurately predict synchronization dynamics in strongly perturbed oscillatory systems.

Main Methods:

  • Decomposing perturbations into a slowly varying component and weak fluctuations.
  • Introducing a generalized phase parameterized by the slowly varying component.
  • Deriving a closed equation for the generalized phase to describe oscillator dynamics.

Main Results:

  • The generalized phase reduction method is applicable to strongly perturbed oscillators.
  • The method accurately predicts synchronization properties, unlike the conventional approach.
  • The approach allows exploration of diverse rhythmic phenomena with large variations.

Conclusions:

  • The generalized phase reduction method offers a powerful tool for studying complex oscillatory systems.
  • This advancement expands the scope of theoretical investigations into rhythmic phenomena.
  • The method provides accurate predictions for synchronization in systems previously intractable with standard techniques.