# Nondegenerate multistationarity in small reaction networks

Source: [Nondegenerate multistationarity in small reaction networks](<https://www.sota2.com/research/paper/68fa54e51e209131ce98f47e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T13:15:35.067Z

Authors: Anne Shiu, Timo de Wolff

Published: 2018-01-31T15:32:08.000Z

## Abstract

Much attention has been focused in recent years on the following algebraic problem arising from applications: which chemical reaction networks, when taken with mass-action kinetics, admit multiple positive steady states? The interest behind this question is in steady states that are stable. As a step toward this difficult question, here we address the question of multiple nondegenerate positive steady states. Mathematically, this asks whether certain families of parametrized, real, sparse polynomial systems ever admit multiple positive real roots that are simple. Our main results settle this problem for certain types of small networks, and our techniques point the way forward for larger networks.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1802.00306>)

[PDF](<https://arxiv.org/pdf/1802.00306.pdf>)