The capture into parametric autoresonance
The capture into parametric autoresonance
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捕获参数自谐振
DOI：
10.1007/s11071-006-9084-2
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发表时间：
2005
影响因子：
5.6
通讯作者：
S. Glebov
中科院分区：
文献类型：
--
作者：
O. Kiselev;S. Glebov
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。我们证明了接近捕获时刻的解由Painlevé-2方程描述。利用渐近展开式的匹配，我们得到了主参数共振方程在捕获前后的渐近解的连接公式。
In this work, we show that the capture into parametric resonance may be explained as pitchfork bifurcation in the primary parametric resonance equation. We prove that the solution close to the moment of the capture is descibed by the Painlevé-2 equation. We obtain connection formulae for the asymptotic solution of the primary parametric resonance equation before and after the capture using the matching of asymptotic expansions.