Speaker
Description
Political instability often exhibits long-term oscillatory patterns, commonly referred to in Structural-Demographic Theory (SDT) as secular cycles. Although existing computational approaches, such as the Multi-Path Forecasting (MPF) framework, can reproduce historical instability trends through high-dimensional simulations, they often lack the analytical tractability needed to clarify the structural mechanisms underlying these oscillations. To address this limitation, we propose a reduced-dimensional continuous-time model consisting of three coupled ordinary differential equations that capture the nonlinear feedback among radicalization, collective violence, and accumulated structural pressure. Using a mean-field approximation for the population reservoir, we derive a minimal dynamical system that preserves the essential structure of the original framework. Stability analysis based on the Routh–Hurwitz criterion shows that equilibrium stability is governed by the rate of exogenous economic decline. We further prove the existence of a supercritical Hopf bifurcation, demonstrating that secular cycles of violence emerge as a stable limit-cycle attractor when structural pressure exceeds a critical threshold. Numerical simulations support the analytical results and provide a rigorous mathematical foundation for the endogenous periodicity of social unrest.
