Bifurcation rigidity

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

Bifurcation rigidity

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

Physics

Research output: Contribution to journal › Article › peer-review

35 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 language	English
Pages (from-to)	35-56
Number of pages	22
Journal	Physica. D, Nonlinear Phenomena
Volume	129
Issue number	1-2
Publication status	Published - 1 May 1999

Keywords

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

Cite this

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title = "Bifurcation rigidity",

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.",

keywords = "bifurcation diagrams, period-doubling bifurcations, saddle-node bifurcations, NON-LINEAR TRANSFORMATIONS, PARAMETER SPACE, SYSTEMS, SETS",

author = "Hunt, {B R} and Gallas, {J A C} and C Grebogi and Yorke, {J A} and H Kocak",

year = "1999",

month = may,

day = "1",

language = "English",

volume = "129",

pages = "35--56",

journal = "Physica. D, Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier",

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TY - JOUR

T1 - Bifurcation rigidity

AU - Hunt, B R

AU - Gallas, J A C

AU - Grebogi, C

AU - Yorke, J A

AU - Kocak, H

PY - 1999/5/1

Y1 - 1999/5/1

N2 - 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.

AB - 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.

KW - bifurcation diagrams

KW - period-doubling bifurcations

KW - saddle-node bifurcations

KW - NON-LINEAR TRANSFORMATIONS

KW - PARAMETER SPACE

KW - SYSTEMS

KW - SETS

M3 - Article

SN - 0167-2789

VL - 129

SP - 35

EP - 56

JO - Physica. D, Nonlinear Phenomena

JF - Physica. D, Nonlinear Phenomena

IS - 1-2

ER -

Bifurcation rigidity

Abstract

Keywords

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