The capture into parametric autoresonance
Mathematical Physics
2007-05-23 v1 Dynamical Systems
math.MP
Abstract
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.
Cite
@article{arxiv.math-ph/0511017,
title = {The capture into parametric autoresonance},
author = {O M Kiselev and S G Glebov},
journal= {arXiv preprint arXiv:math-ph/0511017},
year = {2007}
}
Comments
LaTeX, 21 pages, 3 figures