Journal of Statistical Physics

, Volume 58, Issue 5–6, pp 863–883 | Cite as

A stochastic return map for stochastic differential equations

  • Jeffrey B. Weiss
  • Edgar Knobloch


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 isO(ε) orO(1). The effective noise in the return map has nonzeroO(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.

Key words

Stochastic map stochastic differential equation limit cycle Gaussian colored noise 


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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Jeffrey B. Weiss
    • 1
  • Edgar Knobloch
    • 1
  1. 1.Physics DepartmentUniversity of CaliforniaBerkeley

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