Bifurcation rigidity

Brian R. Hunt, Jason A.C. Gallas, Celso Grebogi, James A. Yorke, Hüseyin Koçak

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

Bifurcation diagrams of periodic windows of scalar maps are often found to be not only topologically equivalent, but in fact to be related by a nearly linear change of parameter coordinates. This effect has been observed numerically for one-parameter families of maps, and we offer an analytical explanation for this phenomenon. We further present numerical evidence of the same phenomenon for two-parameter families, and give a mathematical explanation like that for the one-parameter case.

Original languageEnglish (US)
Pages (from-to)35-56
Number of pages22
JournalPhysica D: Nonlinear Phenomena
Volume129
Issue number1-2
DOIs
StatePublished - May 1 1999

Keywords

  • Bifurcation diagrams
  • Period-doubling bifurcations
  • Saddle-node bifurcations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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