具有衰减扰动与噪声的系统中的非线性共振
Nonlinear resonance in systems with decaying perturbations and noise
AI总结：
本文研究乘性白噪声对时间衰减泵浦非等时系统中共振捕获的影响，结合平均法与随机李雅普诺夫函数给出共振模态随机稳定性条件，并应用于杜芬振子。
摘要：
本文研究了乘性白噪声对具有时间衰减泵浦的非等时系统中共振捕获的影响。假设扰动强度随时间衰减，且其频率渐近恒定。考虑了振幅接近共振值且相位与激励同步的吸引解的出现。分析了这种状态在随机扰动系统中的持续性。通过结合平均方法和构造合适的随机李雅普诺夫函数，推导出保证共振模态在无限或渐近长时间区间上随机稳定性的条件。所提出的理论应用于具有衰减参数激励和噪声的杜芬振子。
英文摘要：
The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically constant. The occurrence of attractive solutions with an amplitude close to the resonant value and a phase synchronized with the excitation are considered. The persistence of such a regime in a stochastically perturbed system is analyzed. By combining the averaging method and the construction of suitable stochastic Lyapunov functions, conditions are derived that guarantee the stochastic stability of the resonant modes on infinite or asymptotically large time intervals. The proposed theory is applied to the Duffing oscillator with decaying parametric excitation and noise.
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