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Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion
Discrete Dynamics in Nature and Society ( IF 1.4 ) Pub Date : 2020-11-20 , DOI: 10.1155/2020/4716064
Chunru Li 1 , Zujun Ma 2
Affiliation  

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.

中文翻译:

新产品创新扩散数学模型的动力学分析

本文提出了一种具有时延相关参数和媒体覆盖率的数学模型,用于描述新产品的扩散过程,其中时延相关参数表示潜在客户决定是否采用新产品的阶段。产品。然后,详细分析了所提出模型的稳定性和Hopf分支。中心流形定理和法则形式理论用于研究分岔周期解的稳定性。此外,进行了数值模拟以研究具有延迟相关参数的模型与具有延迟独立参数的模型之间的差异。结果表明,两种模型之间存在显着差异。
更新日期:2020-11-21
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