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Geometric singular perturbation theory in biological practice
- Source :
- Journal of Mathematical Biology, 60(3), 347-386. Springer Verlag
- Publication Year :
- 2009
- Publisher :
- Springer Science and Business Media LLC, 2009.
-
Abstract
- Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains and explores geometric singular perturbation theory and its use in (biological) practice. The three main theorems due to Fenichel are the fundamental tools in the analysis, so the strategy is to state these theorems and explain their significance and applications. The theory is illustrated by many examples.
- Subjects :
- Singular perturbation
Food Chain
Hydra
Applied Mathematics
Mathematical analysis
Models, Biological
Agricultural and Biological Sciences (miscellaneous)
Singular solution
Predatory Behavior
Modelling and Simulation
Modeling and Simulation
Phase space
Morphogenesis
Animals
Applied mathematics
Invariant (mathematics)
Global structure
Mathematics
Subjects
Details
- ISSN :
- 14321416 and 03036812
- Volume :
- 60
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Biology
- Accession number :
- edsair.doi.dedup.....9be0580b3327d4031d7be9afcd3d09bf