  This paper introduces the class of "strongly endotactic networks", a subclass
of the endotactic networks introduced by G. Craciun, F. Nazarov, and C. Pantea.
The main result states that the global attractor conjecture holds for
complex-balanced systems that are strongly endotactic: every trajectory with
positive initial condition converges to the unique positive equilibrium allowed
by conservation laws. This extends a recent result by D. F. Anderson for
systems where the reaction diagram has only one linkage class (connected
component). The results here are proved using differential inclusions, a
setting that includes power-law systems. The key ideas include a perspective on
reaction kinetics in terms of combinatorial geometry of reaction diagrams, a
projection argument that enables analysis of a given system in terms of systems
with lower dimension, and an extension of Birch's theorem, a well-known result
about intersections of affine subspaces with manifolds parameterized by
monomials.
