一类非线性系统在随机激励下的分叉

Bifurcations of a Class of Nonlinear Systems under Stochastic Excitation

本文研究一类阻尼为线性、弹性恢复力为非线性的振动系统在随机外部激励作用下的随机分叉。文中采用广义稳态势和方法,求解系统响应的稳态联合概率密度函数.在此基础上根据由不变测度定义的随机分叉,讨论了具有权式分叉的确定性非线性系统在随机扰动下的分叉行为。

Stochastic bifurcation of a class of nonlinear vibration systems with linear damping and nonlinear stiffness is discussed under external white noise excitation.Generalizd stationary Potential Method is used to obtain the stationary joint probability density.According to the stochastic bifurcation defined by invariant measure,this paper investigated the stochastic.bifurcation of determined nonlinear systems with pitchfork under external white noise exitation.