Journal
MATHEMATICAL BIOSCIENCES AND ENGINEERING
Volume 16, Issue 5, Pages 5062-5091Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2019255
Keywords
reaction network; dimension reduction; invariant set; multiple time scales
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Funding
- [ANR-17-CE40-0036]
- [DFG-391322026 SYMBIONT]
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On the basis of recent work by Cardin and Teixeira on ordinary differential equations with more than two time scales, we devise a coordinate-independent reduction for systems with three time scales; thus no a priori separation of variables into fast, slow etc. is required. Moreover we consider arbitrary parameter dependent systems and extend earlier work on Tikhonov-Fenichel parameter values - i.e. parameter values from which singularly perturbed systems emanate upon small perturbations - to the three time-scale setting. We apply our results to two standard systems from biochemistry.
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