Slow Passage Through a Pitchfork Bifurcation

This paper deals with a class of second-order differential equations with a slowly varying bifurcation parameter. The parameter slowly varies through a critical value corresponding to a transition from a stable equilibrium to one of the two stable branches of an intersecting parabolic curve. The loc...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:SIAM journal on applied mathematics 1996-06, Vol.56 (3), p.889-918
1. Verfasser: Maree, G. J. M.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:This paper deals with a class of second-order differential equations with a slowly varying bifurcation parameter. The parameter slowly varies through a critical value corresponding to a transition from a stable equilibrium to one of the two stable branches of an intersecting parabolic curve. The local transition behavior is described by the second Painleve transcendent. In this study we predict which branch will be followed after passage of the bifurcation point given the initial state. For that purpose, use is made of averaging methods and of asymptotic matching techniques connecting local solutions valid before, during, and after the transition.
ISSN:0036-1399
1095-712X
DOI:10.1137/S0036139993257399