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Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise
Hiroya Nakao1, Jun-nosuke Teramae, Denis S Goldobin
1Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Chaos (Woodbury, N.Y.)
|October 5, 2010
Summary
This study derives a white-noise Langevin equation for limit-cycle oscillators under colored noise. It details effective drift and diffusion coefficients, revealing anomalous frequency dependence for chaotic noise.
Area of Science:
- Physics
- Nonlinear Dynamics
- Stochastic Processes
Background:
- Limit-cycle oscillators are fundamental in various scientific fields.
- Understanding oscillator dynamics under colored noise is crucial for accurate modeling.
- Previous models often simplify noise or oscillator properties.
Purpose of the Study:
- To derive an effective white-noise Langevin equation for long-time phase dynamics of limit-cycle oscillators.
- To analyze the influence of weak stationary colored noise on oscillator phase.
- To determine effective drift and diffusion coefficients based on oscillator and noise characteristics.
Main Methods:
- Derivation of an effective white-noise Langevin equation.
- Calculation of drift and diffusion coefficients using phase sensitivity and noise correlation functions.
- Explicit computation for sinusoidal phase sensitivity and Gaussian processes.
- Verification through numerical simulations with stochastic and chaotic noise.
Main Results:
- An effective white-noise Langevin equation accurately describes oscillator phase dynamics.
- Drift and diffusion coefficients depend on oscillator phase sensitivity and noise correlation.
- Anomalous frequency dependence of coefficients observed for chaotic noise, linked to its power spectrum.
Conclusions:
- The derived Langevin equation provides a robust framework for analyzing oscillators under colored noise.
- The study highlights the significant impact of noise characteristics on oscillator behavior.
- Chaotic noise introduces unique dynamics not captured by simpler noise models.
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