The Collective Behaviors of Self-Excitation Information Diffusion Processes for a Large Number of Individuals

The opinion dynamics is a complex and interesting process, especially for the systems with a large number of individuals. It is usually hard to describe the evolutionary features of these systems. In some previous works, it has been shown that the self-excitation type model has superior performance in learning and predicting opinions. Following this line, we consider the self-excitation opinion model and study the collective behaviors of the self-excitation model. We propose a Mckean–Vlasov-type integrodifferential equation to describe the asymptotic behaviors of the model and show that the introduced equation, by coupling with the initial distribution, has the ability of capturing the influence of the self-excitation process, which describes the mutually exciting and recurrent nature of individuals. We also find that the steady-state distribution is a “contraction” of the initial distribution in the linear and bounded confidence (DW model) interaction cases, which is different from the results of the model with nonself-excitation interaction.