Retour /Back 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'Orléans
MAPMO
45067 Orléans cedex, FRANCE