Bifurcation-Based Predictive Modelling of Socio-Political Dynamics

where 1\gamma\ge1 tunes concentration (higher \gamma makes the highest score dominate).

3) Algorithm: ensemble simulation + actor attribution

Inputs: calibrated model parameters, initial states P0,T0,E0,H0P_0,T_0,E_0,H_0, noise model, candidate actor scores time series si(t)s_i(t), emergence threshold HcH_c, ensemble size NN.

Pseudo-code:

for k = 1..N:

    simulate X_t^(k) = {P,T,E,H,R} forward to horizon T_max with SDE solver

    record _k = first t where H^(k)(t) > H_c (or _k = if not crossed)

    if _k < :

        record actor selection at _k: sample actor i with probability proportional to s_i(_k)^

end

# Compute emerg probability curve