Order in time Thermodynamic conditions for chemical oscillations

Example 13.6 Order in time Thermodynamic conditions for chemical oscillations Consider the following set of reactions 

The concentrations of initial and final products S and D are maintained at constant values. So, there are two independent variables Xand Y. The klf and klh denote the forward and backward chemical reaction rate constants, respectively. The overall affinity characterizes the thermodynamic state of the chemical system, and is found form 

Within the vicinity of a nonequilibrium (A + 0), the magnitude of the affinity may determine the time behavior of the system  

So that the system will be stable to small disturbances around the steady state if it satisfies the inequality 

These kinetic relations yield the following steady-state solutions 

---