### 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 analyzing 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.

Original language | English (US) |
---|---|

Pages (from-to) | 4860-4863 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 77 |

Issue number | 24 |

State | Published - 1996 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*77*(24), 4860-4863.

**Oscillatory behavior of the rate of escape through an unstable limit cycle.** / Maier, Robert S.; Stein, D. L.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 77, no. 24, pp. 4860-4863.

}

TY - JOUR

T1 - Oscillatory behavior of the rate of escape through an unstable limit cycle

AU - Maier, Robert S.

AU - Stein, D. L.

PY - 1996

Y1 - 1996

N2 - 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 analyzing 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.

AB - 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 analyzing 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.

UR - http://www.scopus.com/inward/record.url?scp=4243831704&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243831704&partnerID=8YFLogxK

M3 - Article

VL - 77

SP - 4860

EP - 4863

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 24

ER -