Quadratic autocatalysis with non-linear decay. II: the effect of incomplete mixing

Isothermal kinetic models based upon quadratic and cubic autocatalysis have been widely investigated as model schemes for a variety of chemical systems. A standard assumption in such models is that the process is being investigated in a continuously fed well-stirred tank reactor. This allows the mathematical model to be idealised as a system of ordinary differential equations. In this paper we relax the assumption that the reactor is well-mixed and employ an established two-parameter model for incomplete mixing. We use this to investigate the consequences of poor mixing upon the static and dynamic multiplicity of the model. We show that the phenomenon of incomplete mixing can reduce the complexity of the steady-state diagram by removing Hopf and limit-point bifurcations from the system. Incomplete mixing may also increase the complexity of the steady-state diagram through the creation of additional Hopf bifurcation points.