期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 252, 期 9, 页码 4786-4841出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2012.01.015
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
类别
资金
- ANR [ANR-09-BLAN-0008-01]
- CRC [701]
- Spectral Structures and Topological Methods in Mathematics at the University of Bielefeld
- Agence Nationale de la Recherche (ANR) [ANR-09-BLAN-0008] Funding Source: Agence Nationale de la Recherche (ANR)
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.
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