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Toric differential inclusions occur as key dynamical systems in the contextof the Global Attractor Conjecture. We introduce the notions of minimalinvariant regions and minimal globally attracting regions for toricdifferential inclusions. We describe a procedure for constructing explicitlythe minimal invariant and minimal globally attracting regions fortwo-dimensional toric differential inclusions. In particular, we obtaininvariant regions and globally attracting regions for two-dimensional weaklyreversible or endotactic dynamical systems (even if they have time-dependentparameters).

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