Newton-Okounkov bodies of chemical reaction systems [article]

Nida Obatake, Elise Walker
2022 arXiv   pre-print
Despite their noted potential in polynomial-system solving, there are few concrete examples of Newton-Okounkov bodies arising from applications. Accordingly, in this paper, we introduce a new application of Newton-Okounkov body theory to the study of chemical reaction networks, and compute several examples. An important invariant of a chemical reaction network is its maximum number of positive steady states, which is realized as the maximum number of positive real roots of a parametrized
more » ... ial system. Here, we introduce a new upper bound on this number, namely the 'Newton-Okounkov body bound' of a chemical reaction network. Through explicit examples, we show that the Newton-Okounkov body bound of a network gives a good upper bound on its maximum number of positive steady states. We also compare this Newton-Okounkov body bound to a related upper bound, namely the mixed volume of a chemical reaction network, and find that it often achieves better bounds.
arXiv:2203.03840v1 fatcat:u7y6xuduz5c2fly5mgizili3ji