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One notion of phase for stochastic oscillators is based on the meanreturn-time (MRT): a set of points represents a certain phase if the mean timeto return from any point in this set to this set after one rotation is equal tothe mean rotation period of the oscillator (irrespective of the startingpoint). For this so far only algorithmically defined phase, we derive hereanalytical expressions for the important class of isotropic stochasticoscillators. This allows us to evaluate cases from the literature explicitlyand to study the behavior of the MRT phase in the limits of strong noise. Wealso 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 generaldiffer from the MRT-isochrons.

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