Prototypes of attractors in four dimensions

G. Baier; Jesper Skovhus Thomsen

doi:10.1103/PhysRevE.48.R4172

Prototypes of attractors in four dimensions

G. Baier, Jesper Skovhus Thomsen

Department of Physics

Research output: Contribution to journal › Journal article › Research › peer-review

361 Downloads (Pure)

Abstract

We study an extension of Duffing's equation to three variables with external forcing. Starting from a phase-space preserving chaos, three prototypes of chaotic attractors with a dimension larger than 3 can be derived. We provide examples of hyperchaos and a ''bifractal'' in a four-dimensional how. The second-order Poincare cross section of hyperchaotic how is qualitatively equivalent to the first-order cross section of Ueda's attractor with the same forcing.

Original language	English
Journal	Physical Review E. Statistical, Nonlinear, and Soft Matter Physics
Volume	48
Issue number	6
Pages (from-to)	R4172-R4174
ISSN	1063-651X
DOIs	https://doi.org/10.1103/PhysRevE.48.R4172
Publication status	Published - 1993

Bibliographical note

Copyright (1993) by the American Physical Society.

Keywords

CHAOS
CHEMICAL-REACTION
HYPERCHAOS

Access to Document

10.1103/PhysRevE.48.R4172

ThomsenFinal published version, 536 KB

http://link.aps.org/doi/10.1103/PhysRevE.48.R4172

OpenUrl availability

Full text

Cite this

@article{68bc9ee986964df99c7cb8f06b52fba4,

title = "Prototypes of attractors in four dimensions",

abstract = "We study an extension of Duffing's equation to three variables with external forcing. Starting from a phase-space preserving chaos, three prototypes of chaotic attractors with a dimension larger than 3 can be derived. We provide examples of hyperchaos and a ''bifractal'' in a four-dimensional how. The second-order Poincare cross section of hyperchaotic how is qualitatively equivalent to the first-order cross section of Ueda's attractor with the same forcing.",

keywords = "CHAOS, CHEMICAL-REACTION, HYPERCHAOS",

author = "G. Baier and Thomsen, {Jesper Skovhus}",

note = "Copyright (1993) by the American Physical Society.",

year = "1993",

doi = "10.1103/PhysRevE.48.R4172",

language = "English",

volume = "48",

pages = "R4172--R4174",

journal = "Physical Review E. Statistical, Nonlinear, and Soft Matter Physics",

issn = "1063-651X",

publisher = "American Physical Society",

number = "6",

}

TY - JOUR

T1 - Prototypes of attractors in four dimensions

AU - Baier, G.

AU - Thomsen, Jesper Skovhus

PY - 1993

Y1 - 1993

N2 - We study an extension of Duffing's equation to three variables with external forcing. Starting from a phase-space preserving chaos, three prototypes of chaotic attractors with a dimension larger than 3 can be derived. We provide examples of hyperchaos and a ''bifractal'' in a four-dimensional how. The second-order Poincare cross section of hyperchaotic how is qualitatively equivalent to the first-order cross section of Ueda's attractor with the same forcing.

AB - We study an extension of Duffing's equation to three variables with external forcing. Starting from a phase-space preserving chaos, three prototypes of chaotic attractors with a dimension larger than 3 can be derived. We provide examples of hyperchaos and a ''bifractal'' in a four-dimensional how. The second-order Poincare cross section of hyperchaotic how is qualitatively equivalent to the first-order cross section of Ueda's attractor with the same forcing.

KW - CHAOS

KW - CHEMICAL-REACTION

KW - HYPERCHAOS

U2 - 10.1103/PhysRevE.48.R4172

DO - 10.1103/PhysRevE.48.R4172

M3 - Journal article

SN - 1063-651X

VL - 48

SP - R4172-R4174

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

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

IS - 6

ER -

Prototypes of attractors in four dimensions

Abstract

Bibliographical note

Keywords

Access to Document

OpenUrl availability

Fingerprint

Cite this