Explosive opinion polarization and depolarization with asymmetric perception

Polarization significantly influences societal divisions across economic, political, religious, and ideological lines. Understanding these mechanisms is key to devising strategies to mitigate such divisions and promote depolarization. Our study examines how asymmetric opinion perception, modeled through nonlinear incidence terms, affects polarization and depolarization within structured communities. In particular, we leverage the fact that the modular structure of the social network yields adjacency matrix eigenvectors with approximately constant values within each community, which enables us to predict the spatial profile of polarization patterns. We demonstrate that such asymmetry leads to explosive polarization and causes a hysteresis effect responsible for abrupt depolarization. We develop a mean-field approximation to explain how nonlinear incidence results in first-order phase transitions and the nature of bifurcations. This approach also helps in understanding how opinions polarize according to underlying social network communities and how these phenomena intertwine with the nature of such transitions. Numerical simulations corroborate the analytical findings.