The Bass Diffusion Model on Finite Barabasi-Albert Networks

Figure 1

Left panel: fraction of new adoptions per unit time in the “link class ” (the subset of all individuals having links), as a function of time, in the Bass innovation diffusion model on a BA network. The parameter of the network (number of child nodes in the preferential attachment scheme) is . The maximum number of links in this example is , while in the comprehensive numerical solutions, whose results are summarized in Figure 2, it is . The adoption peak occurs later for the least connected (and most populated) class with . Right panel: cumulative new adoptions per unit time, as a function of time, compared with the same quantity for the homogeneous Bass model without an underlying network. The peak of the homogeneous Bass model is slightly lower and shifted to the right. For the values of the model parameters and and the measuring unit of time, see Figure 2.