Tropicalization and tropical equilibration of chemical reactions
Abstract
Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial systems with separation are equilibrated when at least two monomials, of opposite signs, have the same order of magnitude and dominate the others. These equilibrations and the corresponding truncated dynamics, obtained by eliminating the dominated terms, find a natural formulation in tropical analysis and can be used for model reduction.
Keywords
Cite
@article{arxiv.1303.3963,
title = {Tropicalization and tropical equilibration of chemical reactions},
author = {Vincent Noel and Dima Grigoriev and Sergei Vakulenko and Ovidiu Radulescu},
journal= {arXiv preprint arXiv:1303.3963},
year = {2013}
}
Comments
13 pages, 1 figure, workshop Tropical-12, Moskow, August 26-31, 2012; in press Contemporary Mathematics