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Computing two-dimensional global invariant manifolds in slow-fast systems

Research output: Working paperWorking paper and Preprints

  • James England
  • B Krauskopf
  • HM Osinga
Original languageEnglish
Publication dateJan 2006
StatePublished

Abstract

We present the GlobalizeBVP algorithm for the computation of two-dimensional stable and unstable manifolds of a vector field. Specifically, we use the collocation routines of AUTO to solve boundary problems that are used during the computation to find the next approximate geodesic level set on the manifold. The resulting implementation is numerically very stable and well suited for systems with multiple time scales. This is illustrated with the test-case example of the well-known Lorenz manifold, and with a slow-fast model of a somatotroph cell

Additional information

Sponsorship: The research of J.E. was supported by grant GR/R94572/01 from the Engineering and Physical Sciences Research Council (EPSRC); B.K. and H.M.O. have been supported by EPSRC Advanced Research Fellowship grants GR/A11649/01, EP/C54403X/1

Research areas

  • stable and unstable manifolds, boundary value problems, slow-fast systems

Documents

Documents

  • 2006

    Preprint (usually an early version) , 2 MB, PDF-document

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  1. Computing two-dimensional global invariant manifolds in slow-fast systems

    Research output: Contribution to journalArticle