Leadership Parameters and Bifurcation of Political Unrest: a Mathematical Formalism with Cases Study

Gap: absence of leadership parameters in bifurcation models.

Contribution: formalism linking seven leadership parameters to systemic stability.

2. Mathematical Formalism

Definition of state variables: Trust (T), Economic Stress (E), Protest Intensity (P), Black Horse Potential (H).

Definition of seven leadership parameters and normalization.

Formal integration of leadership parameters into ODE system.

Derivation of normal form for bifurcation (saddle-node, Hopf).

3. Analytical Derivation

Fixed point analysis.

Jacobian derivation and eigenvalue conditions.

Critical thresholds (_E, _crit) as function of leadership parameters.