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 confidence thresholds when he has no active neighbor, thus strengthening his heterophilous propensity. Moreover, his adaptation algorithm is stopped if there is a minimal number of agents within his similarity interval. The heterogeneity of the model could lead to 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.