A new approach to solve opinion dynamics on complex networks

Abstract In this paper, we use the differential equations to establish the continuous opinion models on the complex networks, so as to observe how the nodes holding different opinions influence each other and how the opinion dynamics evolve. One of nodes in the complex network is selected randomly as a social outcast who opposes the opinions of other nodes and is reacted by the opponents equally. The analytical framework of dynamics on weighted-directed complex networks is proposed. We investigate how the strength and position of social outcast impact the opinion evolution. Then, we analyze how the network structures impact the result of dynamical process. Meanwhile, we propose a periodic description and an analytical method to solve the equation-based models. Finally, a series of experiments are conducted on five kinds of typical weighted-directed complex networks to demonstrate the feasibility and effectiveness of our proposed approach.