  Toric dynamical systems are known as complex balancing mass action systems in
the mathematical chemistry literature, where many of their remarkable
properties have been established. They include as special cases all deficiency
zero systems and all detailed balancing systems. One feature is that the steady
state locus of a toric dynamical system is a toric variety, which has a unique
point within each invariant polyhedron. We develop the basic theory of toric
dynamical systems in the context of computational algebraic geometry and show
that the associated moduli space is also a toric variety. It is conjectured
that the complex balancing state is a global attractor. We prove this for
detailed balancing systems whose invariant polyhedron is two-dimensional and
bounded.
