随机激励下非线性系统稳定性的判定方法与比较

在随机非线性系统稳定性的研究方面,近年来出现了随机Melnikov方法、相流函数法和安全盆法。对于这三种新的理论与计算方法的联系和对比,以仅受高斯白噪声激励下的杜芬系统为例进行了分析与探讨,进而对结果的差别进行了讨论。研究结果表明这三种方法在计算系统的稳定性阀值方面具有一致性。

Comparisons Between The Methods in Determining Stabilitiy of stochastically Nonlinear Systems

For the researches on the stability of stochastically nonlinear systems, there appear some new methods in recent years, such as the stochastic Melnikov function, phase space flux and safe basin method. Making use of the dynamic theory, the Monte-Carlo method and Runge-Kutta algorithm, the relations and comparisons between the three novel methods mentioned above are analyzed via the studies on the typical Duffing oscillatory system excited by Gaussian white noise. The results show the consistency of these three methods in computing the threshold value for chaos onset in the system, and the causes of differences are also discussed.