@online{Kruff_arXiv2010.10129,
TITLE = {Algorithmic Reduction of Biological Networks With Multiple Time Scales},
AUTHOR = {Kruff, Niclas and L{\"u}ders, Christoph and Radulescu, Ovidiu and Sturm, Thomas and Walcher, Sebastian},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2010.10129},
EPRINT = {2010.10129},
EPRINTTYPE = {arXiv},
YEAR = {2020},
ABSTRACT = {We present a symbolic algorithmic approach that allows to compute invariant<br>manifolds and corresponding reduced systems for differential equations modeling<br>biological networks which comprise chemical reaction networks for cellular<br>biochemistry, and compartmental models for pharmacology, epidemiology and<br>ecology. Multiple time scales of a given network are obtained by scaling, based<br>on tropical geometry. Our reduction is mathematically justified within a<br>singular perturbation setting using a recent result by Cardin and Teixeira. The<br>existence of invariant manifolds is subject to hyperbolicity conditions, which<br>we test algorithmically using Hurwitz criteria. We finally obtain a sequence of<br>nested invariant manifolds and respective reduced systems on those manifolds.<br>Our theoretical results are generally accompanied by rigorous algorithmic<br>descriptions suitable for direct implementation based on existing off-the-shelf<br>software systems, specifically symbolic computation libraries and<br>Satisfiability Modulo Theories solvers. We present computational examples taken<br>from the well-known BioModels database using our own prototypical<br>implementations.<br>},
}