An innovation diffusion model for three competitive products (Q1879552)

In this work, an innovation diffusion model describing the dynamics of 3 competing products is studied. When all competitors are using advertisement, a unique interior solution exists. It is shown to be globally asymptotically stable. When only two competitors are using advertisement, two equilibrium solutions are shown to exist: one interior and the other on the boundary. Conditions for each of them to be globally asymptotically stable are derived. When at most one of the competitors use advertisement, only boundary equilibrium solutions exist. Conditions for each of them to be globally asymptotically stable are derived. This work indicates that for the persistence of competitors in some cases advertisement is more important than people's contacts.