Opinion dynamics of improved Hegselmann-Krause model with agent's stubbornness and stubborn agents

In this work, we improve the Hegselmann-Krause model (HK model) by combining the agent's stubbornness and the quantitative impact of stubborn agents on the evolution of other agents’ opinions. We divide stubborn agents into expert stubborn agents, environmentally stubborn agents and intrinsically stubborn agents based on the impact weight and agent's characteristics. We simulate the evolution of opinions of the improved HK model, and find that it is closer to reality. We also study the impact of the influence coefficient and the proportion of intrinsically stubborn agents on the stabilization time, and find that the presence of non-expert stubborn agents reduces the rate of convergence of opinions. Finally, we verify the effectiveness of the improved HK model by two real social events