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Global Dynamics Analysis of Homogeneous New Products Diffusion Model

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  • Shuping Li
  • Zhen Jin

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.

Suggested Citation

  • Shuping Li & Zhen Jin, 2013. "Global Dynamics Analysis of Homogeneous New Products Diffusion Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-6, November.
    • Handle: RePEc:hin:jnddns:158901
    DOI: 10.1155/2013/158901
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    1. Yan, Hong-Sen & Ma, Kai-Ping, 2011. "Competitive diffusion process of repurchased products in knowledgeable manufacturing," European Journal of Operational Research, Elsevier, vol. 208(3), pages 243-252, February.
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    3. Vijay Mahajan & Eitan Muller & Roger A. Kerin, 1984. "Introduction Strategy for New Products with Positive and Negative Word-of-Mouth," Management Science, INFORMS, vol. 30(12), pages 1389-1404, December.
    4. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
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    Cited by:

    1. Xiang Zhong & Juan Zhao & Lu-Xing Yang & Xiaofan Yang & Yingbo Wu & Yuan Yan Tang, 2018. "A dynamic discount pricing strategy for viral marketing," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-19, December.

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