参数自共振的捕获
The capture into parametric autoresonance
摘要：
在这项工作中，我们表明，捕获到参数共振可以解释为干草叉分叉的主要参数共振方程。我们证明了解决方案接近的时刻的捕获所描述的Painleve-2方程。利用渐近展开式的匹配，得到了主参数共振方程在俘获前后渐近解的连接公式。
英文摘要：
In this work we show that the capture into parametric resonance may be explained as the pitchfork bifurcation in the primary parametric resonance equation. We prove that the solution close to the moment of the capture is described by the Painleve-2 equation. We obtain the connection formulas for the asymptotic solution of the primary parametric resonance equation before and after the capture using the matching of the asymptotic expansions.
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