Bifurcation rigidity

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 expl...

Full description

Saved in:
Bibliographic Details
Published in:Physica. D 1999-05, Vol.129 (1-2), p.35-56
Main Authors: Hunt, Brian R., Gallas, Jason A.C., Grebogi, Celso, Yorke, James A., Koçak, Hüseyin
Format: Article
Language:English
Subjects:
Bifurcation diagrams
Period-doubling bifurcations
Saddle-node bifurcations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0167-2789
1872-8022
DOI:10.1016/S0167-2789(98)00201-2