Autonomous bifurcations of a simple bimolecular surface-reaction model

A pair of ordinary differential equations describing the Langmuir-Hinshelwood mechanism of a bimolecular surface reaction is presented as a simple model for a heterogeneously catalysed chemical reaction. Numerical and analytical techniques are combined to determine the possible dynamics of this model, which, even though it consists only of low-order polynomials, exhibits very complicated behaviour. This includes sustained oscillations, which appear or disappear at Hopf bifurcations, turning points on periodic branches, global homoclinic and metacritical Hopf bifurcations and codimension-two bifurcations with double eigenvalues of zero. The emphasis of the presentation is on geometrical representation of the observed dynamics.