中文摘要：

研究了受非高斯色噪声参激的Van der Pol-Duffing振子在平凡解邻域内的随机稳定性。首先利用物理学中已有的经典结果,经过近似处理,将非高斯色噪声简化为Ornstein-Uhlenbeck过程,然后通过尺度变换和线性随机变换得到了与系统响应的矩Lyapunov指数相关的特征方程,通过摄动法求得了矩Lyapunov指数、稳定指标、最大Lyapunov指数的二阶近似解,给出了系统响应p阶矩渐进稳定和几乎肯定渐进稳定的条件。最后通过对数值结果的分析,讨论了噪声参数及系统参数对系统响应矩稳定性的影响。

英文摘要：

In the present paper,the stochastic stability of a Van der Pol-Duffing oscillator that is subjected to a parametric excitation by a non-Gaussian colored noise is investigated.Based on the approximation method,the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process.Via a scale transformation and a linear stochastic transformation,the eigenvalue problem that governing the moment Lyapunov exponent is established.Through a perturbation method, the seconded order approximated analytical results of the moment Lyapunov exponent,the stability index,and the top Laypunov exponent are obtained.In addition,the conditions of almost sure stability and moment stability are given.Finally,through the analytical and numerical results,the influences of the noise parameters and system coefficients on the moment stability are discussed.