Bifurcation rigidity

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

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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
Issue number1-2
Publication statusPublished - 1 May 1999


  • bifurcation diagrams
  • period-doubling bifurcations
  • saddle-node bifurcations
  • 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.