Quadratic autocatalysis with non-linear decay

We provide a detailed, and thorough, investigation into the concentration multiplicity and dynamic stability of a prototype non-linear chemical mechanism: quadratic autocatalysis subject to non-linear decay in a continuously stirred tank reactor. This model was previously investigated in the literature using numerical path-following techniques. The contribution of this study is the application of singularity theory and degenerate Hopf-bifurcation theory to obtain analytical representations of many of the features of interest in this system. In particular, we use these presentations to identify critical values of an unfolding parameter below which specified phenomenon are no longer exhibited.