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Abstract We considertoric dynamical systems, which are also calledcomplex-balanced mass-action systems. These are remarkably stable polynomial dynamical systems that arise from the analysis of mathematical models of reaction networks when, under the assumption of mass-action kinetics, they can give rise tocomplex-balanced equilibria. Given a reaction network, we study theset of parameter valuesfor which the network gives rise to toric dynamical systems, also calledthe toric locusof the network. The toric locus is an algebraic variety, and we are especially interested in its topological properties. We show that complex-balanced equilibriadepend continuouslyon the parameter values in the toric locus, and, using this result, we prove that the toric locus has a remarkableproduct structure: it is homeomorphic to the product of the set of complex-balanced flux vectors and the affine invariant polyhedron of the network. In particular, it follows that the toric locus is acontractible manifold. Finally, we show that the toric locus is invariant with respect to bijective affine transformations of the generating reaction network.