标题： 参数自共振在随机扰动下的稳定性 显示英文标题

标题： Stability of parametric autoresonance under random perturbations

摘要： 一个描述非线性振荡系统中参数自共振初始阶段的数学模型被考虑。 在无限时间处能量无界增长的解与自共振现象相关。 研究了此类解的稳定性。 我们描述了允许的确定性和随机扰动类，使得自共振的稳定性在渐近大的区间内得到保持。 显示英文摘要

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.