Computational aspects of quasi-steady state reduction [ Back ]

15:30 to 16:30
UAB - Dept. Matemàtiques (C1/-128)
Sebastian Walcher
RWTH Aachen


Quasi-steady state reduction is a frequently employed heuristical method for parameter-dependent (ordinary) differential equations in (bio-) chemistry and other areas of application. The usual interpretation of this approach in mathematical terms goes via the classical singular perturbation theory due to Tikhonov and Fenichel, but nontrivial problems remain in the implementation.

In the talk, we dicuss polynomial (or rational) parameter-dependent vector fields (which is not a severe restriction for applications in biochemistry). Our first result discusses an explicit, algorithmically accessible reduction formula for a system with a given "small parameter". The reduced equation naturally lives on a certain algebraic variety. Our second result is about the identification of suitable "small parameters" in a given system; it turns out that this problem is also accessible by algorithmic algebra. Several examples are presented.

This is joint work ith Alexandra Goeke.