Realizations Through Weakly Reversible Networks and the Globally Attracting Locus

Abstract. We investigate the possibility that for any given reaction rate vector [Formula: see text] associated with a network [Formula: see text], there exists another network [Formula: see text] with a corresponding reaction rate vector that reproduces the mass-action dynamics generated by [Formula: see text]. Our focus is on a particular class of networks for [Formula: see text], where the corresponding network [Formula: see text] is weakly reversible. We show that strongly endotactic two-dimensional networks with a two-dimensional stoichiometric subspace, as well as certain endotactic networks under additional conditions, exhibit this property. In particular, we show that being endotactic is necessary for the dynamics of a network to be included in the dynamics of a weakly reversible network. Additionally, we establish a strong connection between this family of networks and the locus in the space of rate constants in which the corresponding dynamics admits globally stable steady states.