Séminaire : Modélisation et Calcul Scientifique

Numerical continuation methods for slow-fast dynamical systems - application to neuronal systems

  • Date : 11/12/2012
  • Lieu : Amphithéâtre Alan Turing
  • Intervenants : Mathieu Desroches, Inria & U. of Bristol, UK
  • Organisateurs : Irène Vignon-Clementel

Numerical continuation refers to a family of numerical schemes of predictor-corrector type, which allow to compute solution branches of nonlinear equations depending on one or several parameters. In this talk, I will start by presenting the essentials of pseudo-arclength continuation in the context of parametrized families of differential equations. I will then explain the advantages of using it for equations with multiple time scales, in particular when computing invariant dynamical objects (slow manifolds) and special solutions (e.g. canard orbits, mixed-mode oscillations, bursting oscillations) by continuing families of well-posed boundary-value problems. I will illustrate this approach with examples of neuronal models, both models for single neurons and coupled systems.

Mots-clés : Modélisation et Calcul Scientifique Séminaire Centre de recherche Inria Paris - Rocquencourt

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