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

Robert S. Maier, D. L. Stein

    Research output: Contribution to journalArticle

    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 languageEnglish (US)
    Pages (from-to)4860-4863
    Number of pages4
    JournalPhysical Review Letters
    Volume77
    Issue number24
    StatePublished - 1996

    Fingerprint

    escape
    cycles
    Fokker-Planck equation
    white noise
    logarithms
    dynamical systems

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

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

    In: Physical Review Letters, Vol. 77, No. 24, 1996, p. 4860-4863.

    Research output: Contribution to journalArticle

    Maier, RS & Stein, DL 1996, 'Oscillatory behavior of the rate of escape through an unstable limit cycle', Physical Review Letters, vol. 77, no. 24, pp. 4860-4863.
    Maier, Robert S. ; Stein, D. L. / Oscillatory behavior of the rate of escape through an unstable limit cycle. In: Physical Review Letters. 1996 ; Vol. 77, No. 24. pp. 4860-4863.
    @article{b7ab43793cfc46d98887f8083e928e21,
    title = "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 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.",
    author = "Maier, {Robert S.} and Stein, {D. L.}",
    year = "1996",
    language = "English (US)",
    volume = "77",
    pages = "4860--4863",
    journal = "Physical Review Letters",
    issn = "0031-9007",
    publisher = "American Physical Society",
    number = "24",

    }

    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 -