The capture into parametric autoresonance

Details The capture into parametric autoresonance The capture into parametric autoresonance

2005-11-04

arxiv.org/abs/math-ph/0511017v1

Physics

Mathematical Physics

LaTeX, 21 pages, 3 figures

Scientific paper

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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