Effects of Internet Sales Promotion on a Differential Advertising Model

Hongyong Jiang ,Junhai Ma

doi:10.1155/2018/8618146

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.

Highlights

Advertising is an audio or visual form of marketing communication that employs an openly sponsored, nonpersonal message to promote or sell a product, service, or idea
Internet sales promotion is introduced into a differential advertising model and investigated quantitatively
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

Summary

Introduction

Advertising is an audio or visual form of marketing communication that employs an openly sponsored, nonpersonal message to promote or sell a product, service, or idea. Many discrete and differential game models are constructed to investigate advertising in recent years. Su et al [10] use the dynamic evolutionary game model and the multiagent modeling simulation to discuss the APQSIS agents equilibrium strategies and the effects of their interactive behaviors on the APQSIS evolutionary stability with asymmetric information. Despite the useful results gained from differential game models in advertising, the complex dynamical behaviors such as periodic solution and bifurcation are rarely investigated in advertising models. With the development of technology, Internet sales promotion has become a major promotion strategy in business management [19] It plays a positive role in promoting the development of firms and can disseminate promotion information to improve the sales level. Internet sales promotion is rarely considered into a differential game model and studied quantitatively.

Model Description

Periodic Solutions and Bifurcation

Sales Promotion Strategy

Numerical Results

Conclusions