Eur. Phys. J. B (2016) 89: 20
https://doi.org/10.1140/epjb/e2015-60933-3

Regular Article

Innovation diffusion on time-varying activity driven networks

¹ Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Six MetroTech Center, Brooklyn, New York 11201, USA
² Dipartimento di Ingegneria Automatica e Informatica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

^a e-mail: alessandro.rizzo@nyu.edu
^b e-mail: mporfiri@nyu.edu

Received: 20 September 2015
Received in final form: 1 December 2015
Published online: 25 January 2016

Abstract

Since its introduction in the 1960s, the theory of innovation diffusion has contributed to the advancement of several research fields, such as marketing management and consumer behavior. The 1969 seminal paper by Bass [F.M. Bass, Manag. Sci. 15, 215 (1969)] introduced a model of product growth for consumer durables, which has been extensively used to predict innovation diffusion across a range of applications. Here, we propose a novel approach to study innovation diffusion, where interactions among individuals are mediated by the dynamics of a time-varying network. Our approach is based on the Bass’ model, and overcomes key limitations of previous studies, which assumed timescale separation between the individual dynamics and the evolution of the connectivity patterns. Thus, we do not hypothesize homogeneous mixing among individuals or the existence of a fixed interaction network. We formulate our approach in the framework of activity driven networks to enable the analysis of the concurrent evolution of the interaction and individual dynamics. Numerical simulations offer a systematic analysis of the model behavior and highlight the role of individual activity on market penetration when targeted advertisement campaigns are designed, or a competition between two different products takes place.