随机扰动下参数自共振的稳定性
Stability of parametric autoresonance under random perturbations
摘要：
考虑了一类具有耗散项的非线性振动系统参数自共振捕获初始阶段的数学模型。在无穷远处能量随时间无限增长的解与自共振现象有关。这种解决方案的稳定性进行了研究。我们描述类容许的确定性和随机扰动，使自共振的稳定性保持在一个渐近大的区间。
英文摘要：
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are associated with the autoresonance phenomenon. Stability of such solutions is investigated. We describe classes of admissible deterministic and random perturbations such that the stability of autoresonance is preserved on an asymptotically large interval.
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