Phase Description of Stochastic Oscillations

TL;DR

This paper presents a novel invariant phase description for stochastic oscillations, enabling a global phase variable even in noisy systems where phase is traditionally ill-defined, with practical numerical methods demonstrated.

Contribution

It generalizes the concept of isophases to stochastic oscillations, providing a method to define and compute a global phase in noisy environments.

Findings

Invariant phase description for stochastic oscillations introduced.

Numerical method for finding isophases demonstrated on example systems.

Applicable to experimental data with irregular oscillations.

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.