随机共振问题Fokker-Planck方程的数值研究

A NUMERICAL STUDY OF THE FOKKER-PLANCK EQUATION FOR STOCHASTIC RESONANCE PROBLEM

本文用有限差分方法对一随机共振的Fokker-Planck方程的主要性质进行了广泛的数值研究。结果表明,当绝热近似条件ωD△V和小信号近似条件A1得到满足时,以往的解析近似理论结果与数值结果符合;当驱动强度增加时,则系统表现出明显的决定性非线性振动行为。然而,就随机共振问题本身而言,绝热近似解析理论概括了在双稳系统中发生的随机共振的主要性质。

The behavior of Fokker-Planck Equation for a stochastic resonance problem is studied by using finite difference schemes. The numerical results coincide with the analytical approximate theory under the conditions of adiabatic approximation ω<<D<<△V and small signal approximation A<<1. Although the system rexhibits evidently deterministic non-linear vibration properties when the amplitude of periodic driving force is large, the adiabatic approximate analytical theory can cover the principal properties of stochastic resonance which occurs in the bistable system.