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

Robert S. Maier and Daniel L. Stein

Working Papers from Santa Fe Institute

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. 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.

Keywords: stochastic escape problem; stochastic exit problem; large fluctuations; stochastic resonance; drift diffusion model; Fokker-Planck equation; eikonal approximation; large deviations; exit location; first passage time; escape rate asymptotics; noise induced transitions; singular perturbation theory; noise induced transitions; singular perturbation theory; oscillatory asymptotics; weak noise asymptotics; most probable exit path; most probable escape path. (search for similar items in EconPapers)
Date: 1996-09
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:wop:safiwp:96-09-076

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