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

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).