The Bass diffusion model on networks with correlations and inhomogeneous advertising. (September 2016)

• Record Type: Journal Article
• Authors: Bertotti, M.L.; Brunner, J.; Modanese, G.
• Is Part Of: Chaos, solitons and fractals. Volume 90(2016)
• Page Start: 55
• Page End: 63
• Publication Date: 2016-09
• Subjects: Innovation diffusion -- Bass equation -- scale-free networks -- correlated networks; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.02.039
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: The Bass model, which is an effective forecasting tool for innovation diffusion based on large collections of empirical data, assumes an homogeneous diffusion process. We introduce a network structure into this model and we investigate numerically the dynamics in the case of networks with link density P ( k ) = c / k γ, where k = 1, …, N . The resulting curve of the total adoptions in time is qualitatively similar to the homogeneous Bass curve corresponding to a case with the same average number of connections. The peak of the adoptions, however, tends to occur earlier, particularly when γ and N are large (i.e., when there are few hubs with a large maximum number of connections). Most interestingly, the adoption curve of the hubs anticipates the total adoption curve in a predictable way, with peak times which can be, for instance when N = 100, between 10% and 60% of the total adoptions peak. This may allow to monitor the hubs for forecasting purposes. We also consider the case of networks with assortative and disassortative correlations and a case of inhomogeneous advertising where the publicity terms are "targeted" on the hubs while maintaining their total cost constant.