Stationary states and multiplicity

The stationary-state solutions are obtained by setting d0p/dr = d0q/dt = 0. These give 

Using the singularity theory approach, we find that the stationary-state locus will display a hysteresis loop provided that 

Again then, we see that if there is no desorption of the reactant P, i.e. if K = 0, the system will display multiplicity, irrespective of the poison Q. 

The reaction processes on the surface are now determined by two coupled equations (12.45) and (12.46). There are two independent concentrations and a cubic non-linearity, hence we expect that Hopf bifurcation may also be a feature of this model. 

For simplicity, we will consider the case without reactant desorption, K = 0, in which analytical expressions for the stationary-state concentrations can be obtained. With K = 0, the stationary-state condition requires 

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