不稳定自谐振模的镇定
Stabilization of unstable autoresonant modes
摘要：
本文建立了一个描述在缓变泵作用下振荡系统捕获自共振初始阶段的数学模型。振幅无限增长的解与自共振现象有关。这种解的稳定性非常重要，因为只有稳定的解才对应于物理上可观察到的运动。我们研究的稳定化问题，我们表明，随时间的振幅逐渐减小的参数扰动可以稳定不稳定的自共振模式。
英文摘要：
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the autoresonance phenomenon. Stability of such solutions is of great importance because only stable solutions correspond to physically observable motions. We study the stabilizing problem and we show that the adiabatically varying parametric perturbation with decreasing amplitude in time can stabilize the unstable autoresonant modes.
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