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arXiv · 1301.6852

Phase Description of Stochastic Oscillations

Justus T. C. Schwabedal·Arkady Pikovsky
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Abstract

We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The approach allows to obtain a global phase variable of noisy oscillations, even in the cases where the phase is ill-defined in the deterministic limit. A simple numerical method for finding the isophases is illustrated for noise-induced switching between two coexisting limit cycles, and for noise-induced oscillation in an excitable system. We also discuss how to determine the isophases for experimentally observed irregular oscillations, providing a basis for a refined phase description of observed oscillatory dynamics.

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Justus T. C. Schwabedal, Arkady Pikovsky. 2013-01-29. Phase Description of Stochastic Oscillations. https://doi.org/10.1103/physrevlett.110.204102

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