Heterogeneous Opinion Dynamics With Confidence Thresholds Adaptation

Heterogeneous bounded confidence opinion dynamics with an adaptation policy of the agents' confidence thresholds is considered. The strategy implemented by each agent consists of increasing his or her confidence thresholds when he or she has no active neighbor, thus strengthening his or her heterophilous propensity. Moreover, his or her adaptation algorithm is stopped if there is a minimal number of agents within his or her similarity interval. The heterogeneity of the model could lead to an interesting scenarios, e.g., steady-state oscillatory behaviors and practical clustering. Sufficient conditions for reaching in finite time a practical consensus are proposed. An upper bound on the maximum number of steady-state practical clusters, which depends on the parameters of the confidence thresholds adaptation algorithm, is obtained. The steady-state behaviors in the presence of one-sided confidence thresholds and stubbornness are discussed. Numerical simulations verify the theoretical results.