Weakly reversible deficiency one realizations of polynomial dynamical systems: an algorithmic perspective

Gheorghe CraciunAbhishek DeshpandeJiaxin Jin

Mar 2023

摘要

Given a dynamical system with polynomial right-hand side, can it be generatedby a reaction network that possesses certain properties? This question isimportant because some network properties may guarantee specific dynamicalproperties, such as existence or uniqueness of equilibria, persistence,permanence, or global stability. Here we focus on this problem in the contextof weakly reversible deficiency one networks. In particular, we describe analgorithm for deciding if a polynomial dynamical system admits a weaklyreversible deficiency one realization, and identifying one if it does exist. Inaddition, we show that weakly reversible deficiency one realizations can bepartitioned into mutually exclusive Type I and Type II realizations, where TypeI realizations guarantee existence and uniqueness of positive steady states,while Type II realizations are related to stoichiometric generators, andtherefore to multistability.

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