On the evaluation of the takeoff time and of the peak time for innovation diffusion on assortative networks. Issue 5 (3rd September 2019)

• Record Type: Journal Article
• Authors: Bertotti, Maria Letizia; Modanese, Giovanni
• Is Part Of: Mathematical and computer modelling of dynamical systems. Volume 25:Issue 5(2019)
• Page Start: 482
• Page End: 498
• Publication Date: 2019-09-03
• Subjects: Innovation diffusion -- Bass model -- assortative networks -- takeoff and peak time; Engineering -- Mathematical models -- Periodicals; Computer simulation -- Periodicals; 515.39
• DOI: 10.1080/13873954.2019.1660997
• Languages: English
• ISSNs: 1387-3954

Abstract

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.