Hunting French Ducks in a Noisy Environment
Berglund, Nils ; Gentz, Barbara ; Kuehn, Christian
arXiv, 1011.3193 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2010-11-14
Classification:  Mathematics - Dynamical Systems,  Mathematics - Probability,  Quantitative Biology - Neurons and Cognition,  37H20, 34E17, 60H10 
@article{1011.3193,
     author = {Berglund, Nils and Gentz, Barbara and Kuehn, Christian},
     title = {Hunting French Ducks in a Noisy Environment},
     journal = {arXiv},
     volume = {2010},
     number = {0},
     year = {2010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1011.3193}
}

Berglund, Nils; Gentz, Barbara; Kuehn, Christian. Hunting French Ducks in a Noisy Environment. arXiv, Tome 2010 (2010) no. 0, . http://gdmltest.u-ga.fr/item/1011.3193/