Innovation diffusion equations on correlated scale-free networks

• The Bass diffusion model can be formulated on scale-free networks.
• In the trickle-down version, the hubs adopt earlier and act as monitors.
• We improve the equations in order to describe trickle-up diffusion.
• Innovation is generated at the network periphery, and hubs can act as stiflers.
• We compare diffusion times, in dependence on the scale-free exponent.

We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up process by introducing heterogeneous publicity coefficients (which can also be negative for the hubs, thus turning them into stiflers) and a stochastic term which represents the erratic generation of innovation at the periphery of the network. The results confirm the robustness of the Bass model and expand considerably its range of applicability.