Continuous Time Opinion Dynamics with Opinion-Network Coevolution

Opinion polarization is a ubiquitous phenomenon in social systems, extensively documented in social media data. Existing models qualitatively demonstrate polarization's emergence through coevolving networks, integrating reinforcing mechanisms and network evolution. However, a comprehensive, quantitative theoretical framework elucidating the generic mechanisms governing polarization remains unexplored. This study uncovers a universal scaling law for opinion distributions, characterized by scaling exponents that categorize social systems into polarization and depolarization phases. We identify two fundamental mechanisms driving polarization dynamics and propose a coevolving framework that concurrently accounts for opinion dynamics and network evolution. Analytical exploration reveals three distinct phases: polarization, partial polarization, and depolarization, with an accompanying phase diagram. Notably, the theory predicts the natural emergence of bi-polarized community structures during the polarized phase, consistent with empirical data from Facebook and Blogosphere. Our theory not only explains empirically observed scaling laws but also offers quantifiable predictions of scaling exponents, providing valuable insights into complex polarization dynamics in social systems.