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Bifurcations dans les systèmes stochastiques multi-échelles
Bifurcations in Stochastic Systems with Multiple Timescales
17/10/2011 - 19/10/2011


Liste des participants / List of participants
Lecture 1: Deterministic fast-slow systems Examples from neuroscience - conduction-based models; slow manifolds, Fenichel theory; dynamic bifurcations: dynamic saddle-node, pitchfork and Hopf bifurcation; example: canards in the Fitzhugh-Nagumo equations

Lecture 2: One-dimensional slowly time-dependent stochastic systems Dynamics near stable equilibrium branches; dynamic saddle-node bifurcation; dynamic pitchfork bifurcation; example: stochastic resonance

Lecture 3: Multidimensional fast-slow systems with noise Dynamics near stable slow manifolds; dynamic Hopf bifurcation; example: elliptic bursting

Lecture 4: Excitable systems Excitability of type I: SNIC bifurcation, Morris-Lecar model, interspike time statistics; excitability of type II: singular Hopf bifurcation, Fitzhugh-Nagumo model, interspike time statistics

Lecture 5: Mixed-mode oscillations Deterministic models: folded node singularity, canards; stochastic case: effect of noise on mixed-mode patterns; Hodgkin-Huxley model

References: Lectures 1, 2, 3 : * Nils Berglund and Barbara Gentz, Noise-Induced Phenomena in Slow-Fast Dynamical Systems. A Sample-Paths Approach. Springer, Probability and its Applications (2006)

Lecture 4 : * Nils Berglund and Barbara Gentz, Stochastic dynamic bifurcations and excitability, in C. Laing and G. Lord, (Eds.), Stochastic methods in Neuroscience, p. 65-93, Oxford University Press (2009)

Lecture 5 : * Mathieu Desroches, John Guckenheimer, Christian Kuehn, Bernd Krauskopf, Hinke Osinga and Martin Wechselberger, Mixed-mode oscillations with multiple time scales, SIAM Review, to appear (2011) * Nils Berglund, Barbara Gentz and Christian Kuehn: Hunting French Ducks in a Noisy Environment, preprint (2010)

Organisateur / Organizer:

Nils BERGLUND
Université d Orleans
MAPMO
45067 Orléans cedex, FRANCE