title: Phase description of stochastic 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 us 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 isophases of observed irregular oscillations, providing a basis for a refined phase description in data analysis.
authors.affiliation: Department of Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany.
authors.forename: Justus T C
authors.initials: JT
authors.lastname: Schwabedal
authors.affiliation: Department of Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany.
authors.forename: Arkady
authors.initials: A
authors.lastname: Pikovsky