A STOCHASTIC RETURN MAP FOR STOCHASTIC DIFFERENTIAL-EQUATIONS

A method is presented for constructing a stochastic return map from a stochastic differential equation containing a locally stable limit cycle and small-amplitude [O(ε)] additive Gaussian colored noise. The construction is valid provided the correlation time is O(ε) or O(1). The effective noise in the return map has nonzero O(ε2) mean and is state dependent. The method is applied to a model dynamical system, illustrating how the effective noise in the return map depends on both the original noise process and the local deterministic dynamics. © 1990 Plenum Publishing Corporation.