Source-only realizations, weakly reversible deficiency one networks and dynamical equivalence

TL;DR

This paper investigates the conditions under which reaction networks can be realized with certain properties, demonstrating that source vertices suffice for finding specific realizations and exploring the non-uniqueness of weakly reversible deficiency one networks.

Contribution

It shows that source vertices are sufficient for finding certain dynamical realizations and characterizes the relationships among weakly reversible deficiency one networks.

Findings

Source vertices suffice for certain realizations.

Weakly reversible deficiency one realizations are not unique.

Characterization of dynamical relationships among network types.

Abstract

Reaction networks can display a wide array of dynamics. However, it is possible for different reaction networks to display the same dynamics. This phenomenon is called dynamical equivalence and makes network identification a hard problem to solve. We show that to find a strongly endotactic, endotactic, consistent, or conservative realization that is dynamically equivalent to the mass-action system generated by a given network, it suffices to consider only the source vertices of the given network. In addition, we show that weakly reversible deficiency one realizations are not unique. We also present a characterization of the dynamical relationships that exist between several types of weakly reversible deficiency one networks.