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

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  • Robert S. Maier
  • Daniel L. Stein

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.

Suggested Citation

  • Robert S. Maier & Daniel L. Stein, 1996. "Oscillatory Behavior of the Rate of Escape through an Unstable Limit Cycle," Working Papers 96-09-076, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:96-09-076
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    Cited by:

    1. Smith, Eric, 2024. "Beyond fitness: The information imparted in population states by selection throughout lifecycles," Theoretical Population Biology, Elsevier, vol. 157(C), pages 86-117.

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