Before revision:  In addition, we define the realization of minimal phenotypic polytopes, phenotypic toric ideals and phenotypic toric varieties as a generalization of the phenotypic polytopes described by M. Savageau, [ 12 ], [ 13 ], [ 14 ]  . The implications of the results here presented is that, in principle, they will facilitate solving large scale genetic-metabolic networks by means of toric algebraic geometry tools as well as facilitate elucidating their dynamics.
After revision:  In addition, we define the realization of minimal phenotypic polytopes, phenotypic toric ideals and phenotypic toric varieties as a generalization of the phenotypic polytopes described by M. Savageau, [ 12 ], [ 13 ], [ 14 ] . Also we studied a synthetic oscillatory network of two genes under diverse environmental control modes, we reproduce S. Savageau results and additionally we obtain an invariant sustained oscillatory region . The implications of the results here presented is that, in principle, they will facilitate solving large scale genetic-metabolic networks by means of toric algebraic geometry tools as well as facilitate elucidating their dynamics.