HAL : hal-00535928, version 1

DOI : 10.1016/j.jde.2012.01.015

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Journal of Differential Equations 252, 9 (2012) 4786-4841

Hunting French Ducks in a Noisy Environment

Nils Berglund 1, Barbara Gentz 2, Christian Kuehn 3

(01/05/2012)

We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations, consisting of alternating large- and small-amplitude oscillations. We quantify the effect of noise and obtain critical noise intensities above which the small-amplitude oscillations become hidden by fluctuations. Furthermore we prove that the noise can cause sample paths to jump away from so-called canard solutions with high probability before deterministic orbits do. This early-jump mechanism can drastically influence the local and global dynamics of the system by changing the mixed-mode patterns.

1 :	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349
2 :	Faculty of Mathematics, University of Bielefeld
	Universität Bielefeld
3 :	Max Planck Institute for the Physics of Complex Systems (MPI-PKS)
	Max-Planck-Institut

Domaine

:

Mathématiques/Systèmes dynamiques Mathématiques/Probabilités Sciences du Vivant/Neurosciences/Neurobiologie

Mots Clés : Singular perturbation – Fast-slow system – Invariant manifold – Dynamic bifurcation – Folded node – Canard – Mixed-mode oscillation – Random dynamical system – First-exit time – Concentration of sample paths

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Contributeur : Nils Berglund <>

Soumis le : Dimanche 14 Novembre 2010, 09:39:47

Dernière modification le : Vendredi 17 Février 2012, 18:08:03