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

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

240 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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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.

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KW - Lorenz equations

KW - Numerical methods

KW - Stable and unstable manifolds

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

Abstract

Keywords

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