Relaxation with disappearance of ignition and extinction

There is another type of time dependence possible in this system. If the inflow concentration of the autocatalyst is adjusted so that b0 - a0, then the ignition and extinction points merge at trcs = (k1ao) 1, with ass = Iu0 Under these special conditions, the coefficient of the term in (Aa)2 in the rate equation, and hence in the denominator of eqn (8.21), becomes zero as well as those of the lower powers in A a. Thus the inverse time dependence disappears, and the only non-zero term governing the decay of perturbation is that in (Aa)3  

Integrating this equation gives a decay (always) which follows an inverse dependence on the square root of the time  

This time dependence is typical of all one-variable systems at a point of disappearance of a hysteresis loop (i.e. for which F = Fx = Fxx = 0 in the terms of 7.3.1). 

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