Non-exponential growth or decay

To determine the response of the cubic autocatalytic system to perturbations in the vicinity of a turning point in the locus, we must return to eqn (8.6). The first two terms (not involving A a) again cancel exactly, because of the stationary-state condition. If we are also at an ignition or extinction point, the tangency condition in any of its forms discussed above ensures that the coefficient of the A a term is also zero. Thus the first non-zero term is that involving (Aa)2  

Integrating the leading-order equation for A a gives an inverse dependence of the perturbation with time  

A similar scenario holds at the ignition point, only there the coefficient is negative, so positive initial perturbations decay back perturbations which decrease the concentration of A grow in time. 

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