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

Maria Letizia Bertotti and Giovanni Modanese

Mathematical and Computer Modelling of Dynamical Systems, 2019, vol. 25, issue 5, 482-498

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.

Date: 2019
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DOI: 10.1080/13873954.2019.1660997

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