期刊
SIAM REVIEW
卷 54, 期 2, 页码 211-288出版社
SIAM PUBLICATIONS
DOI: 10.1137/100791233
关键词
mixed-mode oscillation; singular perturbation; dynamical system
资金
- Engineering and Physical Sciences Research Council (EPSRC) [EP/C54403X/1, EP/E032249/1]
- National Science Foundation
- Department of Energy
- Sydney University
- Center for Applied Mathematics (CAM) at Cornell University
- IGERT of CAM at Cornell University
- Cornell University
- University of Sydney
- Bristol Centre for Applied Nonlinear Mathematics
- Engineering and Physical Sciences Research Council [EP/C54403X/1] Funding Source: researchfish
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1006272] Funding Source: National Science Foundation
- Division Of Computer and Network Systems
- Direct For Computer & Info Scie & Enginr [0832782] Funding Source: National Science Foundation
Mixed-mode oscillations (MMOs) are trajectories of a dynamical system in which there is an alternation between oscillations of distinct large and small amplitudes. MMOs have been observed and studied for over thirty years in chemical, physical, and biological systems. Few attempts have been made thus far to classify different patterns of MMOs, in contrast to the classification of the related phenomena of bursting oscillations. This paper gives a survey of different types of MMOs, concentrating its analysis on MMOs whose small-amplitude oscillations are produced by a local, multiple-time-scale mechanism. Recent work gives substantially improved insight into the mathematical properties of these mechanisms. In this survey, we unify diverse observations about MMOs and establish a systematic framework for studying their properties. Numerical methods for computing different types of invariant manifolds and their intersections are an important aspect of the analysis described in this paper.
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