A survey of methods for computing (UN)stable manifolds of vector fields

B. Krauskopf; H. M. Osinga; E. J. Doedel; M. E. Henderson; J. Guckenheimer; A. Vladimirsky; M. Dellnitz; O. Junge

doi:10.1142/S0218127405012533

A survey of methods for computing (UN)stable manifolds of vector fields

B. Krauskopf
, H. M. Osinga
, E. J. Doedel
, M. E. Henderson
, J. Guckenheimer
, A. Vladimirsky
, M. Dellnitz
, O. Junge

University of Bristol
Concordia University
IBM Research
Cornell University
Universität Paderborn

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

252 Scopus citations

Abstract

The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global stable or unstable manifold of a vector field, where we concentrate on the case of a two-dimensional manifold. All methods are illustrated with the same example - the two-dimensional stable manifold of the origin in the Lorenz system.

Original language	English
Pages (from-to)	763-791
Number of pages	29
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	15
Issue number	3
DOIs	https://doi.org/10.1142/S0218127405012533
State	Published - Mar 2005
Externally published	Yes

Keywords

Lorenz equations
Numerical methods
Stable and unstable manifolds

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10.1142/S0218127405012533

Cite this

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abstract = "The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global stable or unstable manifold of a vector field, where we concentrate on the case of a two-dimensional manifold. All methods are illustrated with the same example - the two-dimensional stable manifold of the origin in the Lorenz system.",

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AU - Guckenheimer, J.

AU - Vladimirsky, A.

AU - Dellnitz, M.

AU - Junge, O.

PY - 2005/3

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AB - The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global stable or unstable manifold of a vector field, where we concentrate on the case of a two-dimensional manifold. All methods are illustrated with the same example - the two-dimensional stable manifold of the origin in the Lorenz system.

KW - Lorenz equations

KW - Numerical methods

KW - Stable and unstable manifolds

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M3 - Article

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A survey of methods for computing (UN)stable manifolds of vector fields

Abstract

Keywords

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