  We consider complex-balanced mass-action systems, or toric dynamical systems.
They are remarkably stable polynomial dynamical systems arising from reaction
networks seen as Euclidean embedded graphs. We study the moduli spaces of toric
dynamical systems, called the toric locus: given a reaction network, we are
interested in the topological structure of the set of parameters giving rise to
toric dynamical systems. First we show that the complex-balanced equilibria
depend continuously on the parameter values. Using this result, we prove that
the toric locus of any toric dynamical system is connected. In particular, we
emphasize its product structure: it is homeomorphic to the product of the set
of complex-balanced flux vectors and the affine invariant polyhedron. Finally,
we show that the toric locus is invariant with respect to bijective affine
transformations of the generating reaction network.
