Analysis of Reaction Network Systems Using Tropical Geometry
Abstract
We discuss a novel analysis method for reaction network systems with polynomial or rational rate functions. This method is based on computing tropical equilibrations defined by the equality of at least two dominant monomials of opposite signs in the differential equations of each dynamic variable. In algebraic geometry, the tropical equilibration problem is tantamount to finding tropical prevarieties, that are finite intersections of tropical hypersurfaces. Tropical equilibrations with the same set of dominant monomials define a branch or equivalence class. Minimal branches are particularly interesting as they describe the simplest states of the reaction network. We provide a method to compute the number of minimal branches and to find representative tropical equilibrations for each branch.
Cite
@article{arxiv.1508.05717,
title = {Analysis of Reaction Network Systems Using Tropical Geometry},
author = {Satya Swarup Samal and Dima Grigoriev and Holger Fröhlich and Ovidiu Radulescu},
journal= {arXiv preprint arXiv:1508.05717},
year = {2015}
}
Comments
Proceedings Computer Algebra in Scientific Computing CASC 2015