Quasi-Toric Differential Inclusions

TL;DR

This paper introduces quasi-toric differential inclusions, a simplified geometric framework closely related to toric differential inclusions, enabling better understanding of weak reversibility and persistence in polynomial dynamical systems.

Contribution

The paper defines quasi-toric differential inclusions, proves their relation to toric inclusions, and shows their applicability to weakly reversible dynamical systems.

Findings

Every toric differential inclusion can be embedded into a quasi-toric differential inclusion.

Every quasi-toric differential inclusion can be embedded into a toric differential inclusion.

Weakly reversible systems can be embedded into quasi-toric differential inclusions.

Abstract

Toric differential inclusions play a pivotal role in providing a rigorous interpretation of the connection between weak reversibility and the persistence of mass-action systems and polynomial dynamical systems. We introduce the notion of quasi-toric differential inclusions, which are strongly related to toric differential inclusions, but have a much simpler geometric structure. We show that every toric differential inclusion can be embedded into a quasi-toric differential inclusion and that every quasi-toric differential inclusion can be embedded into a toric differential inclusion. In particular, this implies that weakly reversible dynamical systems can be embedded into quasi-toric differential inclusions.