  We study families of polynomial dynamical systems inspired by biochemical
reaction networks. We focus on complex balanced mass-action systems, which have
also been called toric. They are known or conjectured to enjoy very strong
dynamical properties, such as existence and uniqueness of positive steady
states, local and global stability, persistence, and permanence. We consider
the class of disguised toric dynamical systems, which contains toric dynamical
systems, and to which all dynamical properties mentioned above extend
naturally. By means of (real) algebraic geometry we show that some reaction
networks have an empty toric locus or a toric locus of Lebesgue measure zero in
parameter space, while their disguised toric locus is of positive measure. We
also propose some algorithms one can use to detect the disguised toric locus.
