Quadratic autocatalysis with non-linear decay (Q460975)

Steady state solutions are sought for model equations of a chemical process in a continuously stirred tank. It is governed by quadratic autocatalysis with a nonlinear catalyst decay. The pertinent model static and dynamics behavior has been previously investigated numerically by using path-following techniques [\textit{J. Brindley} et al., Proc. R. Soc. Lond., Ser. A 417, No. 1853, 463--496 (1988; Zbl 0652.92025)]. The main contribution of the present paper is the application of singularity theory and degenrate Hopf-bifurcation theory to obtain analytical representations for the cusp, isola, double zero and double Hopf point singularities. The bifurcation diagram is obtained that way. Various critical values have been deduced. General criterions were established for static multiplicity and periodic solutions.