Stability of an autocatalytic reaction

Example 12.4 Stability of an autocatalytic reaction For a simple example, we may consider the following autocatalytic reaction, which appears in the reaction scheme of the Brusselator 

We have the forward Jrf = kfcxcY and backward. /rh = khcx reaction rates, respectively. The affinity A and the flow of reaction Jx are 

The excess entropy production can become negative if kf kh. and hence the stationary state may become unstable. 

The study of the behavior of the stationary state of /th order after a disturbance may be helpful for stability considerations. For this purpose, we designate the index 5 for all forces and flows in the stationary state. Assuming that the force Xk has been disturbed by 8Xh and keeping the remaining forces constant, we have 

The first summation term on the right is the minimum entropy production corresponding to the stationary state. The second sum on the right is zero, according to the Onsager reciprocal relations and the Prigogine principle. Therefore, we have 

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