Fractal Basin Boundaries, Long-Lived Chaotic Transients, and Unstable-Unstable Pair Bifurcation

Celso  Grebogi; Edward Ott; James A. Yorke

doi:10.1103/PhysRevLett.50.935

Fractal Basin Boundaries, Long-Lived Chaotic Transients, and Unstable-Unstable Pair Bifurcation

Celso Grebogi, Edward Ott, James A. Yorke

Physics

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

283 Citations (Scopus)

Abstract

A new type of bifurcation to chaos is pointed out and discussed. In this bifurcation two unstable fixed points or periodic orbits are created simultaneously with a strange attractor which has a fractal basin boundary. Chaotic transients associated with the coalescence of the unstable-unstable pair are shown to be extraordinarily long-lived.

Original language	English
Pages (from-to)	935-938
Number of pages	4
Journal	Physical Review Letters
Volume	50
Issue number	13
DOIs	https://doi.org/10.1103/PhysRevLett.50.935
Publication status	Published - 28 Mar 1983

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title = "Fractal Basin Boundaries, Long-Lived Chaotic Transients, and Unstable-Unstable Pair Bifurcation",

abstract = "A new type of bifurcation to chaos is pointed out and discussed. In this bifurcation two unstable fixed points or periodic orbits are created simultaneously with a strange attractor which has a fractal basin boundary. Chaotic transients associated with the coalescence of the unstable-unstable pair are shown to be extraordinarily long-lived.",

author = "Celso Grebogi and Edward Ott and Yorke, {James A.}",

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AU - Grebogi, Celso

AU - Ott, Edward

AU - Yorke, James A.

PY - 1983/3/28

Y1 - 1983/3/28

N2 - A new type of bifurcation to chaos is pointed out and discussed. In this bifurcation two unstable fixed points or periodic orbits are created simultaneously with a strange attractor which has a fractal basin boundary. Chaotic transients associated with the coalescence of the unstable-unstable pair are shown to be extraordinarily long-lived.

AB - A new type of bifurcation to chaos is pointed out and discussed. In this bifurcation two unstable fixed points or periodic orbits are created simultaneously with a strange attractor which has a fractal basin boundary. Chaotic transients associated with the coalescence of the unstable-unstable pair are shown to be extraordinarily long-lived.

U2 - 10.1103/PhysRevLett.50.935

DO - 10.1103/PhysRevLett.50.935

M3 - Article

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VL - 50

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EP - 938

JO - Physical Review Letters

JF - Physical Review Letters

IS - 13

ER -

Fractal Basin Boundaries, Long-Lived Chaotic Transients, and Unstable-Unstable Pair Bifurcation

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