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We introduce positively transverse reaction networks, a class of chemical reaction systems defined by a geometric property of their constituent polytopes. Under mass-action kinetics, we prove that no bounded trajectory with positive initial conditions can converge to a boundary omega-limit point. This finding establishes a fundamental persistence property for trajectories within these specific network structures.
Positively transverse reaction networks guarantee that trajectories starting with positive concentrations will never reach a state where any species is extinct.
We introduce positively transverse reaction networks and show that, with mass-action kinetics, no bounded trajectory with positive initial condition has a boundary omega-limit point. These networks are characterized by a geometric property of a collection of polytopes defined by a subset of complexes of the network.