Locus of boundary crisis: Expect inifinitely many gaps

HM Osinga

doi:10.1103/PhysRevE.74.035201

Locus of boundary crisis: Expect inifinitely many gaps

HM Osinga

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Abstract

Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of the boundary crisis is associated with curves of homoclinic or heteroclinic bifurcations of periodic saddle points. It is known that this locus has nondifferentiable points. We show here that the locus of boundary crisis is far more complicated than previously reported. It actually contains infinitely many gaps, corresponding to regions (of positive measure) where attractors exist.

Translated title of the contribution	Locus of boundary crisis: Expect inifinitely many gaps
Original language	English
Pages (from-to)	035201(R)
Number of pages	4
Journal	Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume	74
DOIs	https://doi.org/10.1103/PhysRevE.74.035201
Publication status	Published - Sept 2006

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Publisher: American Physical Soc

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title = "Locus of boundary crisis: Expect inifinitely many gaps",

abstract = "Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of the boundary crisis is associated with curves of homoclinic or heteroclinic bifurcations of periodic saddle points. It is known that this locus has nondifferentiable points. We show here that the locus of boundary crisis is far more complicated than previously reported. It actually contains infinitely many gaps, corresponding to regions (of positive measure) where attractors exist.",

author = "HM Osinga",

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AU - Osinga, HM

N1 - Publisher: American Physical Soc

PY - 2006/9

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N2 - Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of the boundary crisis is associated with curves of homoclinic or heteroclinic bifurcations of periodic saddle points. It is known that this locus has nondifferentiable points. We show here that the locus of boundary crisis is far more complicated than previously reported. It actually contains infinitely many gaps, corresponding to regions (of positive measure) where attractors exist.

AB - Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of the boundary crisis is associated with curves of homoclinic or heteroclinic bifurcations of periodic saddle points. It is known that this locus has nondifferentiable points. We show here that the locus of boundary crisis is far more complicated than previously reported. It actually contains infinitely many gaps, corresponding to regions (of positive measure) where attractors exist.

U2 - 10.1103/PhysRevE.74.035201

DO - 10.1103/PhysRevE.74.035201

M3 - Article (Academic Journal)

SN - 1550-2376

SN - 2470-0053

VL - 74

SP - 035201(R)

JO - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

ER -

Locus of boundary crisis: Expect inifinitely many gaps

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