WIAS Preprint No. 411, (1998)

Regular oscillations in systems with stochastic resonance



Authors

  • Milstein, Grigori N.
  • Tretyakov, Michael V.

2010 Mathematics Subject Classification

  • 60H10 93E30

Keywords

  • Noise-driven monostable, bistable and coupled bistable systems, periodic forcing, boundary value problems of parabolic type, numerical integration of stochastic differential equations

Abstract

Constructive sufficient conditions for regular oscillations in systems with stochastic resonance are given. For bistable systems, they rely on the fact that the probability of transition of a point from one well to the other with subsequent stay there during the half-period of the periodic forcing is close to 1. Using these conditions, domains of parameters corresponding to the regular oscillations are indicated. The regular oscillations are considered in bistable and monostable systems with additive and multiplicative noise. Special attention is paid to numerical methods. Algorithms based on numerical integration of stochastic differential equations turn out to be most natural both for simulation of sample trajectories and for solution of related boundary value problems of parabolic type. Results of numerical experiments are presented.

Appeared in

  • Physica D Nonlinear Phenomena, vol./issue: 140/3-4, (2000), pp. 244-256, under new title: Numerical analysis of noise-induced regular oscillations.

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