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Stochastically perturbed limit cycles

Published online by Cambridge University Press:  14 July 2016

Charles J. Holland
Charles J. Holland*
Affiliation:
Purdue University
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Abstract

In this paper we examine the effects of perturbing certain deterministic dynamical systems possessing a stable limit cycle by an additive white noise term with small intensity. We place assumptions on the system guaranteeing that when noise is present the corresponding random process generates an ergodic probability measure. We then determine the behavior of the invariant measure when the noise intensity is small.

Keywords

STOCHASTIC DIFFERENTIAL EQUATIONSLIMIT CYCLESERGODIC MEASURES
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 311 - 320
Copyright
Copyright © Applied Probability Trust 1978 

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References

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