Pitchfork bifurcations of invariant manifolds

Document Type

Article

Publication Date

4-15-2007

Abstract

A pitchfork bifurcation of an (m - 1)-dimensional invariant submanifold of a dynamical system in Rm is defined analogous to that in R. Sufficient conditions for such a bifurcation to occur are stated and existence of the bifurcated manifolds is proved under the stated hypotheses. For discrete dynamical systems, the existence of locally attracting manifolds M+ and M-, after the bifurcation has taken place is proved by constructing a diffeomorphism of the unstable manifold M. Techniques used for proving the theorem involve differential topology and analysis. The theorem is illustrated by means of a canonical example. © 2007 Elsevier B.V. All rights reserved.

Identifier

34047155544 (Scopus)

Publication Title

Topology and Its Applications

External Full Text Location

https://doi.org/10.1016/j.topol.2006.12.014

ISSN

01668641

First Page

1650

Last Page

1663

Issue

8

Volume

154

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