具有衰减啁啾频率激励和噪声的非线性系统中的共振
Resonances in nonlinear systems with a decaying chirped-frequency excitation and noise
AI总结：
研究乘性白噪声下强非线性振荡系统在啁啾频率激励中的共振捕获问题，通过平均化方法与随机 Lyapunov 函数分析共振模态的随机稳定性，并应用于 Duffing 振荡器。
摘要：
研究了乘性白噪声对强非线性振荡系统在啁啾频率激励下共振捕获的影响。假设扰动强度随时间多项式衰减，且其频率按幂律增长。考虑了振幅和相位随激励同步增长的共振解。讨论了在随机扰动存在时该状态的持久性。特别地，描述了保证共振模态在无限或渐近大时间区间上随机稳定性的条件。所用技术结合了平均化方法、稳定性分析和随机 Lyapunov 函数的构造。将所提理论应用于具有啁啾频率激励和噪声的 Duffing 振荡器。
英文摘要：
The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially with time, and its frequency grows according to a power low. Resonant solutions with a growing amplitude and phase, synchronized with the excitation, are considered. The persistence of such a regime in the presence of stochastic perturbations is discussed. In particular, conditions are described that guarantee the stochastic stability of the resonant modes on infinite or asymptotically large time intervals. The technique used is based on a combination of the averaging method, stability analysis and construction of stochastic Lyapunov functions. The proposed theory is applied to the Duffing oscillator with a chirped-frequency excitation and noise.
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