Theory and application of a nongeneric heteroclinic loop bifurcation

Shui Nee Chow, Bo Deng, Mark J. Friedman

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Homoclinic and heteroclinic bifurcations from a heteroclinic loop are considered. The system under consideration has three parameters, two of which are not suitable for generic unfoldings. Analytical criteria in terms of derivatives to Melnikov's functions are given for nongeneric parameters. Four qualitatively distinct bifurcation diagrams are obtained. The result is used to give an explanation of a numerical finding on the generation of traveling pulsing waves in a two-phase flow problem.

Original languageEnglish (US)
Pages (from-to)1303-1321
Number of pages19
JournalSIAM Journal on Applied Mathematics
Volume59
Issue number4
StatePublished - Jan 1 1999

Fingerprint

Melnikov Function
Homoclinic
Bifurcation Diagram
Two-phase Flow
Unfolding
Two phase flow
Traveling Wave
Two Parameters
Bifurcation
Derivatives
Distinct
Derivative

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Theory and application of a nongeneric heteroclinic loop bifurcation. / Chow, Shui Nee; Deng, Bo; Friedman, Mark J.

In: SIAM Journal on Applied Mathematics, Vol. 59, No. 4, 01.01.1999, p. 1303-1321.

Research output: Contribution to journalArticle

Chow, Shui Nee ; Deng, Bo ; Friedman, Mark J. / Theory and application of a nongeneric heteroclinic loop bifurcation. In: SIAM Journal on Applied Mathematics. 1999 ; Vol. 59, No. 4. pp. 1303-1321.
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