2. Parameter estimation --- use a combination of:
Time-series fitting (extended Kalman filter / particle filter) for online updating.
Bayesian MCMC for posterior distributions of uncertain parameters.
System identification with multiple scenario calibrations.
3. Simulation & scenario testing --- Monte Carlo ensembles over stochastic forcings (\xi) and parameter ranges to produce probabilistic forecasts (e.g., probability that P>PcP> P_c within 30/90 days; probability that H>HcH>H_c).
7) Diagnostics & early-warning indices
From the model we can construct practical indicators:
Critical slowing down: rising autocorrelation and variance of PP and TT signal approach to a bifurcation.
r-index: the real-time estimate of r=K/Ur=\rho_{\mathcal{K}}/\rho_U from observed policy responses; trending upward is a danger signal.
H-lead: growth rate of HH (dH/dt) --- rapid positive values indicate imminent political emergence.
The above system is intentionally modular: nonlinear threshold functions and saturating policy responses allow both qualitative bifurcation analysis and quantitative simulation. The model is not a black-box predictor --- it is a mechanistic early-warning toolkit that, when calibrated with timely data, yields probabilistic scenario maps and policy sensitivity analyses useful to decision makers and researchers alike.
B. Interaction Structure and Feedback Loops
We organize the dynamics into reinforcing (R) and balancing (B) feedbacks that couple the state variables---trust TT, economic stress EE, protest intensity PP, black-horse potential HH, resilience RR---with the policy controls: accommodative U(t)U(t) and coercive K(t)\mathcal{K}(t). These loops explain how small shocks can amplify into regime shifts (bifurcations) or be absorbed.
1) Core reinforcing loops (destabilizing)
R1: Stress Unrest Stress
