Determining ``small parameters'' for quasi-steady state (Q2343531)

The authors are interested in the mathematical analysis of quasi-steady state phenomena arising in the systems parameter-dependent ordinary differential equations of the form \[ \dot x=h(x,\pi),\;x\in\mathbb{R}^n, \;\pi\in \mathbb{R}^m, \] where \(h\) is smooth in the variables \((x,\pi).\) Primarily, the authors were interested in the case when \(h\) is a rational or polynomial function as it is in the standard Michaelis-Menten reaction, for example. They introduce the notion of a Tikhonov-Fenichel parameter value (TFPV) as a parameter tuple such that every small deviation will lead to a singular perturbation scenario for which Tikhonov's and Fenichel's theorems are applicable. A computational approach to finding TFPVs via elimination ideals applied to some systems is described. This approach also supports the use of algorithmic algebra techniques.