The Iterative Persuasion-Polarization Opinion Dynamics and Its Mean-Field Analysis

.In this paper, we introduce the iterative persuasion-polarization (IPP) model to study the dynamics of opinion formation and change within a population. The IPP model integrates mechanisms of persuasion and repulsion, where individuals influence one another through interactions that can either align opinions incrementally or lead to greater divergence. The probability of each interaction type is governed by a parameter \(α\), representing the population's receptiveness to persuasion. We investigate how these interaction dynamics shape the long-term distribution of opinions, examining conditions that promote consensus or polarization. By deriving a system of nonlinear and autonomous ordinary differential equations (ODEs), we provide a rigorous mathematical framework for analyzing the distributional behavior of opinions in large populations. Our findings contribute to a deeper understanding of social influence dynamics and their implications in complex social systems.Keywordssociophysicsagent-based modelopinion dynamicsinteracting agentsmean-fieldMSC codes91D2591D3082C3182C2235Q91