Dynamics of Limit Cycle Oscillator Subject to General Noise

Abstract

The phase description is a powerful tool for analyzing noisy limit cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to the Gaussian noise while noise in the real world often has non-Gaussian statistics. Here, we provide the phase reduction for limit cycle oscillators subject to general, colored and non-Gaussian, noise including heavy-tailed noise. We derive quantifiers like mean frequency, diffusion constant, and the Lyapunov exponent to confirm consistency of the result. Applying our results, we additionally study a resonance between the phase and noise.

main paper: 4 pages, 2 figure; auxiliary material: 5-7 pages of the document, 1 figure

References in corpus (4)

• Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
• Stochastic phase reduction for a general class of noisy limit cycle oscillators
• Phase reduction of stochastic limit cycle oscillators
• Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses

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