Stochastic phase reduction for a general class of noisy limit cycle oscillators

Abstract

We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit cycle. The equation naturally includes previously proposed and mutually exclusive phase equations as special cases. The validity of the theory is numerically confirmed. Using the method, we reveal how noise and its correlation time affect limit cycle oscillations.

10 pages, 2 figures

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• Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
• Phase reduction of stochastic limit cycle oscillators
• Collective Phase Sensitivity
• Temporal precision of spike response to fluctuating input in pulse-coupled networks of oscillating neurons

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