加性二值噪声激励下Duffing系统的随机分岔

Stochastic Bifurcations in a Duffing System Driven by Additive Dichotom ous Noises

研究了Duffing系统在加性二值噪声作用下的随机分岔现象.首先,根据二值噪声的统计特性,推导得到二值噪声状态间的跃迁概率,据此对二值噪声进行了数值模拟.其次,利用四阶Runge-Kutta(龙格-库塔)数值算法得到该系统位移和速率的稳态联合概率密度及位移的稳态概率密度.然后,通过对位移稳态概率密度单双峰结构变化的研究,发现加性二值噪声的状态和强度能够诱导系统产生随机分岔现象.最后,观察到随着系统非对称参数的逐渐变化,系统同样产生了随机分岔现象.

The stochastic bifurcations in a Duffmg system driven by additive dichotomous noises were investigated. Firstly, the transition probability of the dichotomous noise states was deduced according to its statistical properties and then the dichotomous noise was simulated numerically. Secondly, the stationary joint probability density of the system displacement and speed and the stationary probability density of the displacement were calculated with the 4th-order Runge-Kutta algorithm. Then, through the study of the variation between unimodality and bimodality of the stationary probability density of the system displacement, it is found that specific states and certain intensity values of the additive dichotomous noise may induce stochastic bifurcations. Lastly, it is also observed that stochastic bifurcations may occur with the variations of the system asymmetric parameters.