  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 each other through interactions that can either align opinions
incrementally or lead to greater divergence. The probability of each
interaction type is governed by a parameter $\alpha$, 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.
