Calculation of Relative Stability in a Two-Variable Example, the Selkov Model

4 Calculation of Relative Stability in a Two-Variable Example, the Selkov Model 

In this section we compare the predictions of the thermod50iamic theory for relative stability in a two-variable example, the Selkov model, with the results obtained from numerical integration of the reaction diffusion equation. The model, constructed for early studies of glycolysis, has two variables, X and Y, and two constant concentrations. The reaction mechanism is 

A and B, and the ratio of the diffusivities S = Dy/D - In Fig. 5.4 we show an example of the solutions of the reaction diffusion equations for this system. 

The predictions of the thermodynamic theory presented in this chapter for equistability of two stable stationary states for the Selkov model is shown in Fig. 5.6. The results of the theory run parallel to the calculations and approach them as the length of the interface region is increased. To show this quantitatively we define the relative error 

I numerical result — theoretical result numerical result 

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