The coevolution dynamics between opinion and stubbornness based on heterogeneous agents

This study investigates the coevolution dynamics between opinion and stubbornness among heterogeneous agents on Barabási-Albert networks using a modified Hegselmann-Krause model. In this modified model, stubbornness is coupled with opinion, allowing agents to impact their stubbornness based on opinion differences from their neighbors. By introducing the concept of opinion tolerance M, we study the simultaneous interaction between opinion and stubbornness dynamics, wherein stubbornness is constantly modulated based on the opinion difference between the agent and its neighbors, thereby further impacting the subsequent opinion dynamics. The results demonstrate that higher M, representing lower opinion tolerance, leads to more fragmented stubbornness clusters, smaller relative size of the largest stubbornness cluster and lower stubbornness convergence time. However, higher M values do not directly alter the opinion clustering but prolong opinion convergence time. In addition, recognizing the heterogeneity of agents in the real world, we divide the group into three categories: open-minded-, moderate-minded- and close-minded-agents. The study further investigates how the proportions of different agent types impact the coevolution dynamics between opinion and stubbornness. Moreover, network with a high average degree is conducive to stubbornness and opinion clustering. Ultimately, our findings indicate that an increase in network size results in a diminished impact on the formation of opinion and stubbornness clustering, while simultaneously extends the convergence time of the underlying dynamics. This study provides significant contributions to advancing the understanding of public opinion dynamics.