Effects of Internet Sales Promotion on a Differential Advertising Model

Abstract

Advertising and sales promotion are two important specific marketing communications tools. In this paper, Internet sales promotion is introduced into a differential advertising model and investigated quantitatively. The conditions for the existence and stability of periodic solutions are obtained. Flip bifurcation of periodic solution is investigated analytically. The results show that the sales promotion parameter can modify the stability of the differential advertising model and lead to chaos through flip bifurcation, the sales level will eventually be no less than a given value by adjusting the value of the sales promotion parameter, and the optimal sales promotion strategy can lead to maximum profit. Numerical results for periodic solutions, bifurcation diagrams, and the effects of sales promotion strategies, which are illustrated with an example, are in good agreement with the theoretical analysis. These results have certain significant theoretical and practical value in related markets.