Simple models and oscillations in closed systems

Chapter 2 will discuss in some detail a simple isothermal autocatalytic model whereby a reactant P is converted to a product C through two intermediates A and B. The simple kinetic model can be written as 

The rates of the first and last steps (the initial production of A from P and the final conversion of B to C) are taken simply to be first order. 

From the above scheme we may easily write down the law of mass action equations for the rates of change of the concentrations p, a, and b  

These equations can be rearranged to give the stationary-state concentrations 

We can also find the simple expression for the concentration of the reactant as a function of time by integrating eqn(1.33) to give 

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