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

B Krauskopf, HM Osinga, EJ Doedel, ME Henderson, J Guckenheimer, A Vladimirsky, M Dellnitz, O Junge

Research output: Working paperWorking paper and Preprints

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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.
Original languageEnglish
Publication statusUnpublished - 2004

Bibliographical note

Additional information: Preprint submitted to the International Journal of Bifurcation and Chaos

Sponsorship: The authors thank Mike Jolly for providing the image in Fig. 3 of the Lorenz manifold computed with the method in [Johnson et al., 1997] and seen from the common viewpoint.

Keywords

  • unstable manifolds
  • Lorenz equation
  • stable manifolds
  • numerical methods

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