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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 158901, 6 pages
http://dx.doi.org/10.1155/2013/158901
Research Article

Global Dynamics Analysis of Homogeneous New Products Diffusion Model

Shuping Li1,2 and Zhen Jin2,3

1School of Mechatronic Engineering, North University of China, Taiyuan 030051, China
2Department of Mathematics, North University of China, Taiyuan 030051, China
3Complex Systems Center, Shanxi University, Taiyuan 030006, China

Received 4 June 2013; Revised 3 October 2013; Accepted 4 October 2013

Academic Editor: Sarangapani Jagannathan

Copyright © 2013 Shuping Li and Zhen Jin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A mathematical model with stage structures is presented that incorporates the awareness stage and the decision-making stage; individuals exchange product information by two channels: mass media and interpersonal communication. When the persuasive advertisement is neglected in the decision-making stage, we find a threshold value about whether new products diffusion is successful or not. When the persuasive advertisement is considered, there must exist a positive equilibrium under some parameter condition; moreover, it must be globally asymptotically stable as long as it exists. Results show that the persuasive advertisement in the decision-making stage does not influence new products' successful diffusion, but the critical value that new products diffuse successfully decreases when the persuasive advertisement is considered. Some numerical simulations confirm our theoretical analysis and demonstrate the influence of parameters on the system. Corresponding to the analysis results, some diffusion strategies are provided.