Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 259, Issue 3, Pages 1149-1180Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2015.02.038
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Funding
- DFG Research Training Group Experimental and Constructive Algebra [GRK 1632]
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For a parameter-dependent system of ordinary differential equations we present a systematic approach to the determination of parameter values near which singular perturbation scenarios (in the sense of Tikhonov and Fenichel) arise. We call these special values Tikhonov-Fenichel parameter values. The principal application we intend is to equations that describe chemical reactions, in the context of quasi-steady state (or partial equilibrium) settings. Such equations have rational (or even polynomial) right-hand side. We determine the structure of the set of Tikhonov-Fenichel parameter values as a semi-algebraic set, and present an algorithmic approach to their explicit determination, using Groebner bases. Examples and applications (which include the irreversible and reversible Michaelis-Menten systems) illustrate that the approach is rather easy to implement. (C) 2015 Elsevier Inc. All rights reserved.
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