Bifurcation rigidity

B R Hunt, J A C Gallas, C Grebogi, J A Yorke, H Kocak

Research output: Contribution to journalArticle

34 Citations (Scopus)

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. (C) 1999 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)35-56
Number of pages22
JournalPhysica. D, Nonlinear Phenomena
Volume129
Issue number1-2
Publication statusPublished - 1 May 1999

Keywords

  • bifurcation diagrams
  • period-doubling bifurcations
  • saddle-node bifurcations
  • NON-LINEAR TRANSFORMATIONS
  • PARAMETER SPACE
  • SYSTEMS
  • SETS

Cite this

Hunt, B. R., Gallas, J. A. C., Grebogi, C., Yorke, J. A., & Kocak, H. (1999). Bifurcation rigidity. Physica. D, Nonlinear Phenomena, 129(1-2), 35-56.

Bifurcation rigidity. / Hunt, B R ; Gallas, J A C ; Grebogi, C ; Yorke, J A ; Kocak, H .

In: Physica. D, Nonlinear Phenomena, Vol. 129, No. 1-2, 01.05.1999, p. 35-56.

Research output: Contribution to journalArticle

Hunt, BR, Gallas, JAC, Grebogi, C, Yorke, JA & Kocak, H 1999, 'Bifurcation rigidity', Physica. D, Nonlinear Phenomena, vol. 129, no. 1-2, pp. 35-56.
Hunt BR, Gallas JAC, Grebogi C, Yorke JA, Kocak H. Bifurcation rigidity. Physica. D, Nonlinear Phenomena. 1999 May 1;129(1-2):35-56.
Hunt, B R ; Gallas, J A C ; Grebogi, C ; Yorke, J A ; Kocak, H . / Bifurcation rigidity. In: Physica. D, Nonlinear Phenomena. 1999 ; Vol. 129, No. 1-2. pp. 35-56.
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