  This paper concerns the long-term behavior of population systems, and in
particular of chemical reaction systems, modeled by deterministic mass-action
kinetics. We approach two important open problems in the field of Chemical
Reaction Network Theory, the Persistence Conjecture and the Global Attractor
Conjecture. We study the persistence of a large class of networks called
lower-endotactic and in particular, we show that in weakly reversible
mass-action systems with two-dimensional stoichiometric subspace all bounded
trajectories are persistent. Moreover, we use these ideas to show that the
Global Attractor Conjecture is true for systems with three-dimensional
stoichiometric subspace.
