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On the evaluation of the takeoff time and of the peak time for innovation diffusion on assortative networks

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  • Maria Letizia Bertotti
  • Giovanni Modanese

Abstract

This paper deals with a generalization of the Bass model for the description of the diffusion of innovations. The generalization keeps into account heterogeneity of the interactions of the consumers and is expressed by a system of several nonlinear differential equations on complex networks. The following contributions can be singled out: first, explicit algorithms are provided for the construction of various families of assortative scale-free networks; second, a method is provided for the identification of the takeoff time and of the peak time, which represent important turning points in the life cycle of an innovation/product; third, the emergence of specific patterns in connection with networks of the same family is observed, whose tentative interpretation is then given. Also, a comparison with an alternative approach is given, within which adoption times of different communities are evaluated of a network describing firm cooperations in South Tyrol.

Suggested Citation

  • Maria Letizia Bertotti & Giovanni Modanese, 2019. "On the evaluation of the takeoff time and of the peak time for innovation diffusion on assortative networks," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 25(5), pages 482-498, September.
    • Handle: RePEc:taf:nmcmxx:v:25:y:2019:i:5:p:482-498
    DOI: 10.1080/13873954.2019.1660997
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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.
    2. Tian Liang & Bin Yang & Chenning Deng & Ping Du & Tuqiang Wang & Hongxing Zhou & Panpan Wang & Jingjing Yu & Aizhong Ding & Fujun Ma & Qingbao Gu & Fasheng Li, 2022. "Diffusion of Cement Kiln Co-Processing of Contaminated Soil in Selected Provinces of China: Engineering Practices, Modeling, and Driving Factors," Sustainability, MDPI, vol. 14(22), pages 1-13, November.
    3. Giovanni Modanese, 2023. "The Network Bass Model with Behavioral Compartments," Stats, MDPI, vol. 6(2), pages 1-13, March.
    4. L. Lucchio & G. Modanese, 2024. "Diffusion on assortative networks: from mean-field to agent-based, via Newman rewiring," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(10), pages 1-15, October.

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