On the steady-state behaviour of the autocatalator model A + 2B⇌3B, B⇌C in a continuous-flow stirred-tank reactor

The steady-state behaviour of the ‘ autocatalator ’ model A + 2B⇌3B B⇌C in a continuous-flow stirred-tank reactor (CSTR) with flow rate as the bifurcation variable is investigated. It is shown that the model gives rise to a structurally stable singularity provided none of the rate constants is zero and all the species are present in the feed stream. When the inlet concentration of species A is greater than three times that of species C, there exist 14 stable bifurcation diagrams. Some of these bifurcation diagrams contain three different ranges of flow rates in which multiplicity exists. When the inlet concentration of species A is smaller than three times that of C, the organizing centre for the autocatalator is a winged cusp. The unfolding of this singularity gives seven stable bifurcation diagrams, which also exist for the physical system. In this case, the behaviour of the autocatalator is qualitatively the same as that of the classical problem of a single exothermic reaction in a CSTR.