Highest-order singularities and unfoldings

The cusp described by eqn (7.60) meets the hysteresis line 0O = i at the point 0o = i, k2 = 27/256, when simultaneously 

For the model in the absence of decay, the highest-order singularity in the system is that for which 

This corresponds to an ordinary cusp, with an unfolding to a unique locus or a single hysteresis loop. 

Now that the recipes for locating the various changes in the qualitative form of the stationary-state locus have been presented, we can go on to examine the origin of the behaviour in the cubic autocatalytic system with the additional uncatalysed step, and for the non-adiabatic non-isothermal CSTR which has been asserted in previous sections. 

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