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arXiv · 2412.17798

The generic geometry of steady state varieties

Elisenda Feliu·Oskar Henriksson·Beatriz Pascual-Escudero
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Abstract

We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give an ideal-theoretic characterization of generic absolute concentration robustness, as well as conditions under which a network that admits multiple steady states also has the capacity for nondegenerate multistationarity. The key tools underlying our results come from the theory of vertically parametrized systems, and include a linear algebra condition that characterizes when the steady state system has positive nondegenerate zeros.

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Elisenda Feliu, Oskar Henriksson, Beatriz Pascual-Escudero. 2024-12-23. The generic geometry of steady state varieties. https://arxiv.org/abs/2412.17798

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