An analytical approach to the Mean--Return-Time~Phase of isotropic stochastic oscillators

Abstract

One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean rotation period of the oscillator (irrespective of the starting point). For this so far only algorithmically defined phase, we derive here analytical expressions for the important class of isotropic stochastic oscillators. This allows us to evaluate cases from the literature explicitly and to study the behavior of the MRT phase in the limits of strong noise. We also use the same formalism to show that lines of constant return time variance (instead of constant mean return time) can be defined, and that they in general differ from the MRT-isochrons.

arXiv comment5 pages, 4 figures

References in corpus (8)

• Predator-prey cycles from resonant amplification of demographic stochasticity
• Active phase and amplitude fluctuations of flagellar beating
• Frequency and Phase Synchronization in Stochastic Systems
• Phase Description of Stochastic Oscillations
• Asymptotic Phase for Stochastic Oscillators
• Phase descriptions of a multidimensional Ornstein-Uhlenbeck process
• Effects of moderate noise on a limit cycle oscillator: Counter rotation and bistability
• A Random Dynamical Systems Perspective on Isochronicity for Stochastic Oscillations