Hunting French ducks in a noisy environment

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Berglund, Nils¹  Gentz, Barbara²  Kuehn, Christian³ 

[1] Univ Orleans, CNRS, MAPMO, UMR 6628,FR 2964, F-45067 Orleans 2, France

[2] Univ Bielefeld, Fac Math, D-33501 Bielefeld, Germany

[3] Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany

关键词: 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;   

DOI  :  10.1016/j.jde.2012.01.015

来源: Elsevier

【 摘 要 】

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 beyond 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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free