HOPF-BIFURCATION IN AN ADVERTISING DIFFUSION-MODEL

The paper presents a two-state diffusion model for repeat purchasing. It recognizes (1) the interaction between customers and potential buyers and (2) the Dorfman-Steiner result for constant elasticities which says that a monopolist will advertise until the ratio of dollar advertising to dollar sales is constant. Using stability analysis conditions are derived under which the variables show oscillatory behaviour. In particular, the occurrence of limit cycles is shown by means of Hopf bifurcation theory. The message of the paper is that the combination of widely accepted assumptions and rules of marketing behaviour may produce persistent fluctuations in sales and advertising over time.