Algorithmic Reduction of Biological Networks with Multiple Time Scales - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematics in Computer Science Year : 2021

Algorithmic Reduction of Biological Networks with Multiple Time Scales


We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular biochemistry, and compartmental models for pharmacology, epidemiology and ecology. Multiple time scales of a given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within a singular perturbation setting. The existence of invariant manifolds is subject to hyperbolicity conditions, for which we propose an algorithmic test based on Hurwitz criteria. We finally obtain a sequence of nested invariant manifolds and respective reduced systems on those manifolds. Our theoretical results are generally accompanied by rigorous algorithmic descriptions suitable for direct implementation based on existing off-theshelf software systems, specifically symbolic computation libraries and Satisfiability Modulo Theories solvers. We present computational examples taken from the well-known BioModels database using our own prototypical implementations.
Fichier principal
Vignette du fichier
Kruff2021_Article_AlgorithmicReductionOfBiologic.pdf (1.1 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03438176 , version 1 (21-11-2021)




Niclas Kruff, Christoph Lüders, Ovidiu Radulescu, Thomas Sturm, Sebastian Walcher. Algorithmic Reduction of Biological Networks with Multiple Time Scales. Mathematics in Computer Science, 2021, 15 (3), pp.499 - 534. ⟨10.1007/s11786-021-00515-2⟩. ⟨hal-03438176⟩
61 View
51 Download



Gmail Mastodon Facebook X LinkedIn More