On the persistence and global stability of mass-action systems (Q2902734)

The author is concerned with the long-term behavior of population systems, and, in particular, of chemical reaction systems, modeled by deterministic mass-action kinetics. He approaches two important open problems in the field of chemical reaction network theory: the persistence conjecture and the global attractor conjecture. He studies the persistence of a large class of networks called lower-endotactic and, in particular, shows that in weakly reversible mass-action systems with two-dimensional stoichiometric subspace, all bounded trajectories are persistent. Moreover, he uses these ideas to show that the global attractor conjecture is true for systems with three-dimensional stoichiometric subspace.