Pitchfork bifurcations of invariant manifolds

Jyoti Champanerkar, Denis Blackmore

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1650-1663
Number of pages14
JournalTopology and its Applications
Volume154
Issue number8
DOIs
StatePublished - Apr 15 2007

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Bifurcation
  • Invariant manifolds
  • Pitchfork bifurcation

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