Spreading dynamics of a well-known brand recognition model on scale-free networks

Abstract

In order to study the influence of the comment mechanism and the heterogeneity of underlying networks on the spreading of well-known brands' recognition, we present a new SFAD (Susceptible-Favorite-Amnesic-Disliked) well-known brands' recognition spreading model based on scale-free network. By using the mean-field theory, the spreading dynamics of the model is analyzed in detail. Then, the basic reproductive number  and equilibriums are derived. The relationships among the basic reproduction number , favorite rate, dislike rate are studied. Furthermore, the global stability of the information-elimination equilibrium the permanence of well-known brands' recognition spreading are proved in detail. Numerical simulations are performed to confirm the analytical results