The capture into parametric autoresonance
Kiselev, O M ; Glebov, S G
arXiv, 0511017 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-11-04
Classification:  Mathematical Physics,  Mathematics - Dynamical Systems,  70K28,  70K50,  35B40 
@article{0511017,
     author = {Kiselev, O M and Glebov, S G},
     title = {The capture into parametric autoresonance},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511017}
}

Kiselev, O M; Glebov, S G. The capture into parametric autoresonance. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511017/