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

James England, B Krauskopf, HM Osinga

Research output: Working paperWorking paper and Preprints

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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
Original languageEnglish
Publication statusPublished - Jan 2006

Bibliographical note

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

Keywords

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

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