Mixed Hegselmann-Krause Dynamics III - Li, Hsin-Lun (Communications in Mathematics and Applications, 2025)
The mixed Hegselmann-Krause (HK) model encompasses both the Deffuant and HK models. Building upon our previous work (Mixed Hegselmann-Krause dynamics II, Discrete and Continuous Dynamical Systems - B 28(5) (2023), 2981 – 2993), we delve into the mixed HK model within a heterogeneous interaction framework. This involves either pair interaction, where all interacting pairs approach each other equally at their rate, or group interaction at each time step. Our research focuses on identifying circumstances conducive to consensus formation within this heterogeneous interaction paradigm. Furthermore, we delve into pair interaction scenarios where interacting pairs can approach each other at distinct rates. This differs from the Deffuant model, where an interacting pair can only approach each other at the same rate under a homogeneous threshold. Our investigation also aims to elucidate the conditions under which consensus can be attained under pair interaction with distinct approaching rates.