A survey of method's for computing (un)stable manifold 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 method's for computing (un)stable manifold of vector fields

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

Atoms, Molecules, Lasers

Research output: Contribution to Journal › Article › Academic › peer-review

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
Volume	15
Issue number	3
DOIs	https://doi.org/10.1142/S0218127405012533
Publication status	Published - 2005

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title = "A survey of method's for computing (un)stable manifold of vector fields",

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 - Krauskopf, B.

AU - Osinga, H.M.

AU - Doedel, E.J.

AU - Henderson, M.E.

AU - Guckenheimer, J.

AU - Vladimirsky, A.

AU - Dellnitz, M.

AU - Junge, O.

PY - 2005

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N2 - 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.

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.

U2 - 10.1142/S0218127405012533

DO - 10.1142/S0218127405012533

M3 - Article

SN - 0218-1274

VL - 15

SP - 763

EP - 791

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

IS - 3

ER -

A survey of method's for computing (un)stable manifold of vector fields

Abstract

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