噪声对杜芬振子的混沌性质的影响

本文对一经典杜芬振子在周期激励及白噪声同时作用下的混沌性质进行分析，文中首先用分段线性模型逼近原型，并采用分段积分理论得到Ｆ－Ｐ方程的封闭解，对概率密度函数及均值相轨线，功率谱及庞加来图的分析，指出系统在有限时间内呈类似“混沌随机”性质，并通过随机稳定性讨论对所揭示的物理现象作了分析。

Influence of Noise on the Chaotic Behaviour of a Duffing Oscillator

In this paper the chaotic behaviour of a classical Duffing oscillator under a combination of periodic and white noise excitation is studied. Using a piecewise linear model to approach to the original model, we deride the close form solutions of F-P equation by adopting the piecewise integration theory. Through analysing the probability density function, mean trajectory,power spectrum and mean Poincare map, we show that the system exhibits chaotic stochastic behaviour in a finite time. Baged on the discussion of stochastic stability, the above revealed Physical phenomenon is interpreted.