有界随机噪声激励下软弹簧Duffing振子的安全盆分叉

研究了软弹簧Duffing振子在有界随机噪声激励下，系统安全盆的侵蚀现象，并提出了随机安全盆分叉的概念. 计算表明，由于随机扰动的影响，系统的随机安全盆分叉点发生了偏移. 关键词： Duffing振子 有界随机噪声 安全盆 分叉

Bifurcation of safe basins in softening Duffing oscillator under bounded noise excitation

The erosion of the safe basins of a softening Duffing oscillator under harmonic or bounded random noise is studied in detail using the Monte-Carlo method. As an alternative, stochastic bifurcation may be defined as a sudden change in the character of the stochastic safe basin when the bifurcation parameter of the system passes through a critical value. This definition applies equally well either to randomly perturbed motion, or to purely deterministic motion. It is found that random noise may destroy the integrity of safe basins and bring about stochastic bifurcation, hence make the system more unsafe.