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arXiv · 2407.01760

Understanding Multistationarity of Fully Open Reaction Networks

Shenghao Yao·AmirHosein Sadeghimanesh·Matthew England
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Abstract

This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon the existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we provide a novel deterministic operation to generate new non-multistationary networks. This is interesting because while there were many operations to create infinitely many new multistationary networks from a multistationary example, this is the first such operation for the non-multistationary counterpart. Such tools for the generation of example networks have a use-case in the application of data science to reaction network theory. We demonstrate this by using the new data, along with a novel graph representation of reaction networks that is unique up to a permutation on the name of species of the network, to train a graph attention neural network model to predict multistationarity of reaction networks. This is the first time machine learning tools are used for studying classification problems of reaction networks.

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Shenghao Yao, AmirHosein Sadeghimanesh, Matthew England. 2024-07-01. Understanding Multistationarity of Fully Open Reaction Networks. https://doi.org/10.1007/s11538-025-01537-8

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