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Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion

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  • Chunru Li
  • Zujun Ma

Abstract

In this paper, a mathematical model with time-delay-related parameters and media coverage to describe the diffusion process of new products is proposed, in which the time-delay-related parameters denote the stage in which potential customers decide whether to adopt a new product. Then, the stability and the Hopf bifurcation of the proposed model are analyzed in detail. The center manifold theorem and the normal form theory are used to investigate the stability of the bifurcating periodic solution. Moreover, a numerical simulation is conducted to investigate the difference between the model with delay-dependent parameters and that with delay-independent parameters. The results show that there is significant difference between the two models.

Suggested Citation

  • Chunru Li & Zujun Ma, 2020. "Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-13, November.
    • Handle: RePEc:hin:jnddns:4716064
    DOI: 10.1155/2020/4716064
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    Cited by:

    1. Sergei Sidorov & Alexey Faizliev & Vladimir Balash & Olga Balash & Maria Krylova & Aleksandr Fomenko, 2021. "Extended innovation diffusion models and their empirical performance on real propagation data," Journal of Marketing Analytics, Palgrave Macmillan, vol. 9(2), pages 99-110, June.

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