随机驱动摆稳定性的出现：超越Kapitsa效应
Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect
摘要：
本文考虑了一个典型的可由乘性噪声镇定的非线性系统：一个带有随机振动支点的欠阻尼非线性摆。数值求解了相应的Fokker-Planck方程，结果表明，即使在白噪声条件下，摆的上平衡点也能稳定，不存在“Kapitsa摆”效应。稳定发生在一个强噪声的制度，WKB近似不成立。
英文摘要：
We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the "Kapitsa pendulum" effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.
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