Document Type

Article

Department/Program

Mathematics

Journal Title

Journal of Functional Analysis

Pub Date

2013

Volume

264

Issue

10

First Page

2269

Abstract

It is proved that a symmetry-breaking bifurcation occurs at a simple eigenvalue despite the usual transversality condition fails, and this bifurcation from a degenerate simple eigenvalue result complements the classical one with the transversality condition. The new result is applied to an imperfect pitchfork bifurcation, in which a forward transcritical bifurcation changes to a backward one when the perturbation parameter changes. Several applications in ecological and genetics models are shown. (C) 2013 Elsevier Inc. All rights reserved.

DOI

10.1016/j.jfa.2013.02.010

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