The Dynamics of Polarization: Four Phases of Attractor Collapse in Societies

Polarization is not simply ideological distance or partisan hostility—it is a four-phase attractor-collapse process driven by the spectral evolution of social-influence networks. We present a unified dynamical framework in which individual drift, homophilic interaction, and network susceptibility jointly determine ideological trajectories. Three diagnostics—the dominant eigenvalue of the influence matrix (χ), a variance–divergence ratio (VDR¹), and center density—capture the geometry and stability of ⁻attractor basins.Applying this framework to the complete roll-call history of the U.S. Congress (1789–2024; N=50,829 member-terms), we identify a 91-year polarization trajectory beginning with the New Deal. The diagnostics reveal a consistent sequence: dimensional compression, geometric sorting, dynamical tightening, and intra-attractor fragmentation. This progression recovers canonical party-system transitions without labels and explains the collapse of moderation: once χ exceeds a critical threshold χ_c, social forces overwhelm intrinsic drift, rendering autonomous moderation dynamically unstable.Comparative analysis shows the same four-phase sequence across revolutions, authoritarian consolidations, and digital communities, with timescales governed by network connectivity and coupling strength. These results suggest polarization is a predictable dynamical outcome of influence networks, offering a general mechanism for understanding democratic instability, factionalism, and ideological entrapment across diverse political systems.A reference implementation and all experimental code are available