Oscillatory Behavior of the Rate of Escape through an Unstable Limit Cycle (1996)
| Citations: | 4 - 0 self |
BibTeX
@MISC{Maier96oscillatorybehavior,
author = {Robert Maier and D. L. Stein},
title = {Oscillatory Behavior of the Rate of Escape through an Unstable Limit Cycle},
year = {1996}
}
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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. PACS numbers: 02.50.-r, 05.40.+j Typeset using REVT E X A particularly interesting phenomenon is the occurrence of noise-induced transitions between attractors of a dynamical system. Such transitions occur in chemical physics, where the transition is a motion across a transition-state surfac...
Citations
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| 1 | Dykman et al - I - 1995 |
| 1 | FIGURES -3-2 -1 0 1 2 3 -3 -2 -1 x v MPEP W W FIG. 1. The unstable limit cycle @\Omega of the van der Pol model, and the MPEP, which emerges from the attractor (0; 0) and spirals into it. The trajectories exiting from\Omega are optimal trajectories that a - Lett - 1996 |
