Visualizing the structure of chaos in the Lorenz system

HM Osinga; B Krauskopf

Visualizing the structure of chaos in the Lorenz system

HM Osinga, B Krauskopf

Department of Engineering Mathematics

Research output: Working paper › Working paper and Preprints

328 Downloads (Pure)

Abstract

The Lorenz attractor, with its characteristic butterfly shape, has become a much published symbol of chaos. It can be computed by simply integrating (virtually) any initial point. However, it is much more difficult to understand how the Lorenz attractor organizes the dynamics in a global way. We use a recently developed algorithm to compute a complicated two-dimensional surface called the stable manifold. Visualization tools are key to conveying its intricate geometry and beauty, which in turn provides insight into the structure of chaos in the Lorenz system.

Original language	English
Publication status	Published - 2001

Bibliographical note

Additional information: Preprint of a paper later published by Pergamon-Elsevier Science (2002), Computers and Graphic-UK, 26(5), pp.815-823, ISSN 0097-8493

Access to Document

Bcanm 2001r12Submitted manuscript, 544 KB
WarningSubmitted manuscript, 176 bytes

http://hdl.handle.net/1983/502

Fingerprint Dive into the research topics of 'Visualizing the structure of chaos in the Lorenz system'. Together they form a unique fingerprint.

Cite this

@techreport{0a11bc97278a4dabb780dd320bf34339,

title = "Visualizing the structure of chaos in the Lorenz system",

abstract = "The Lorenz attractor, with its characteristic butterfly shape, has become a much published symbol of chaos. It can be computed by simply integrating (virtually) any initial point. However, it is much more difficult to understand how the Lorenz attractor organizes the dynamics in a global way. We use a recently developed algorithm to compute a complicated two-dimensional surface called the stable manifold. Visualization tools are key to conveying its intricate geometry and beauty, which in turn provides insight into the structure of chaos in the Lorenz system.",

author = "HM Osinga and B Krauskopf",

note = "Additional information: Preprint of a paper later published by Pergamon-Elsevier Science (2002), Computers and Graphic-UK, 26(5), pp.815-823, ISSN 0097-8493 ",

year = "2001",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Visualizing the structure of chaos in the Lorenz system

AU - Osinga, HM

AU - Krauskopf, B

N1 - Additional information: Preprint of a paper later published by Pergamon-Elsevier Science (2002), Computers and Graphic-UK, 26(5), pp.815-823, ISSN 0097-8493

PY - 2001

Y1 - 2001

N2 - The Lorenz attractor, with its characteristic butterfly shape, has become a much published symbol of chaos. It can be computed by simply integrating (virtually) any initial point. However, it is much more difficult to understand how the Lorenz attractor organizes the dynamics in a global way. We use a recently developed algorithm to compute a complicated two-dimensional surface called the stable manifold. Visualization tools are key to conveying its intricate geometry and beauty, which in turn provides insight into the structure of chaos in the Lorenz system.

AB - The Lorenz attractor, with its characteristic butterfly shape, has become a much published symbol of chaos. It can be computed by simply integrating (virtually) any initial point. However, it is much more difficult to understand how the Lorenz attractor organizes the dynamics in a global way. We use a recently developed algorithm to compute a complicated two-dimensional surface called the stable manifold. Visualization tools are key to conveying its intricate geometry and beauty, which in turn provides insight into the structure of chaos in the Lorenz system.

M3 - Working paper and Preprints

BT - Visualizing the structure of chaos in the Lorenz system

ER -