A polarization opinion model inspired by bounded confidence communications

This paper proposes a novel opinion dynamics model grounded in the concept of bounded confidence interactions among agents. Our objective is to explain the polarization effects inherent to vector-valued opinions. The evolutionary process adheres to the rule where each agent aspires to increase polarization through communication with a single friend during each discrete time step. The friend is taken from a group of all agents in that way that his opinion is the target opinion of the considered agent. The introduced model can potentially explain the emergence of leaders or leading opinions within groups that actively pursue polarization as a central objective, including politics, fan clubs, and social networks. The dynamics ensure that agents' ultimate (temporal) configuration will encompass a finite number of outlier states. We introduce deterministic and stochastic models, accompanied by a comprehensive mathematical analysis of their inherent properties. Furthermore, we provide compelling illustrative examples and introduce a stochastic solver tailored for scenarios featuring an extensive set of agents. In the context of smaller agent populations, we scrutinize the suitability of neural networks for the rapid inference of limit configurations.