Suppose the stable system has rate parameter β1 = β3 = 22.2, β2 = β4 = 1.39, kinetic-order parameters g32 = -2, g12 = g14 = g54 = 1. If in practice only the rate parameters βi can be varied, the question is how best to construct an oscillatory system. The bifurcation diagram for the model is shown in Figure 7, where it can be seen that for the nominal values of gjk the system is stable and far away from the line of Hopf bifurcation. The inverse bifurcation question is: do there exist parameters βi such that the system is oscillatory? We consider the problem with the following parameter constraints: