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

Journal Article · Sun Dec 01 04:00:00 EST 1996 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.77.4860· OSTI ID:399888

Maier, R S; Stein, D L ^[1]

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1. Department of Mathematics, University of Arizona, Tucson, Arizona 85721 (United States)

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. {copyright} {ital 1996 The American Physical Society.}

• DOE Contract Number: FG03-93ER25155
• OSTI ID: 399888
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 24 Vol. 77; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DYNAMICAL SYSTEMS
FOKKER-PLANCK EQUATION
LIMIT CYCLE
NOISE
NONEQUILIBRIUM
PARAMETRIC OSCILLATORS
POTENTIALS
RESONANCE
STOCHASTIC PROCESSES
STRENGTH FUNCTIONS
TWO-DIMENSIONAL CALCULATIONS