噪声存在下的参数自共振捕获
Capture into parametric autoresonance in the presence of noise
AI总结：
该研究针对含噪声的参数自共振捕获问题，分析振荡系统自共振初始阶段微分方程的无界振幅解，证明白噪声扰动下满足噪声强度条件时，参数自共振捕获以趋于1的概率保持。
摘要：
本文研究了描述振荡系统进入参数自共振初始阶段的微分方程组。其中特别受关注的是振幅随时间无界增长的解。系统被捕获进入自共振的可能性与这类解的稳定性相关。我们研究了自共振解对白噪声类型持续扰动的稳定性，并证明在噪声强度满足特定条件时，系统被捕获进入参数自共振的现象以趋于1的概率得以保持。
英文摘要：
System of differential equations describing the initial stage of the capture of oscillatory systems into the parametric autoresonance is considered. Of special interest are solutions whose amplitude increases without bound with time. The possibility of capture the system into the autoresonance is related with the stability of such solutions. We study the stability of autoresonant solutions with respect to persistent perturbations of white noise type, and we show that under certain conditions on the intensity of the noise, the capture into parametric autoresonance is preserved with probability tending to one.
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