Oscillatory Behavior of the Rate of Escape through an Unstable Limit Cycle

Abstract

Suppose a two-dimensional dynamical system has a stable attractor that is surrounded by an unstable limit cycle. If the system is additively perturbed by white noise, the rate of escape through the limit cycle will fall off exponentially as the noise strength tends to zero. By analysing the associated Fokker-Planck equation we show that in general, the weak-noise escape rate is non-Arrhenius: it includes a factor that is periodic in the logarithm of the noise strength. The presence of this slowly oscillating factor is due to the nonequilibrium potential of the system being nondifferentiable at the limit cycle. We point out the implications for the weak-noise limit of stochastic resonance models.

arXiv comment4 pages, REVTeX, uses epsf macros to include 2 PS figures

References in corpus (4)

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• A Scaling Theory of Bifurcations in the Symmetric Weak-Noise Escape Problem
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• The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance

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