Extending Slow Manifolds Near a Degenerate Transcritical Intersection in Three Dimensions

  • Christine GavinEmail author
  • Philip J. Aston
  • Gianne Derks
Conference paper
Part of the Trends in Mathematics book series (TM, volume 8)


Motivated by a problem from pharmacology, we consider a general two parameter slow–fast system in which the critical set consists of a one dimensional manifold and a two dimensional manifold, intersecting transversally at the origin. Using geometric desingularisation, we show that for a subset of the parameter set there is an exchange of stabilities between the attracting components of the critical set and the direction of the continuation can be expressed in terms of the parameters.


Dimensional Manifold Centre Manifold Slow Manifold Singular Perturbation Theory Attractive Part 
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CG was supported in this work by the EPSRC Doctoral Training Grant 1363360. GD thanks the Centre de Recerca Matemàtica for the opportunity to discuss the work with other participants in the Intensive Research Program on Advances in Nonsmooth Dynamics.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Christine Gavin
    • 1
    Email author
  • Philip J. Aston
    • 1
  • Gianne Derks
    • 1
  1. 1.Department of MathematicsUniversity of SurreyGuildfordUK

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