Minimal invariant regions and minimal globally attracting regions for toric differential inclusions

TL;DR

This paper introduces minimal invariant and globally attracting regions for toric differential inclusions, providing explicit constructions in two dimensions, which aids understanding of dynamical systems related to the Global Attractor Conjecture.

Contribution

It defines new concepts of minimal invariant and attracting regions and offers explicit methods for two-dimensional cases, advancing the analysis of toric dynamical systems.

Findings

Explicit construction of minimal invariant regions in 2D

Explicit construction of minimal globally attracting regions in 2D

Applicable to weakly reversible or endotactic systems with time-dependent parameters

Abstract

Toric differential inclusions occur as key dynamical systems in the context of the Global Attractor Conjecture. We introduce the notions of minimal invariant regions and minimal globally attracting regions for toric differential inclusions. We describe a procedure for constructing explicitly the minimal invariant and minimal globally attracting regions for two-dimensional toric differential inclusions. In particular, we obtain invariant regions and globally attracting regions for two-dimensional weakly reversible or endotactic dynamical systems (even if they have time-dependent parameters).