Normalization: E_c = 0 indicates fractured elite networks and frequent defections, while E_c = 1 indicates cohesive and loyal elite coalitions.
7. Repression versus Consensus Balance (R)
Definition: The strategic mix between coercive repression and consensual inclusion in handling dissent.
Normalization: R = 0 represents reliance on pure repression (high risk of backfire), while R = 1 represents a balanced and calibrated approach where coercion is minimal and consensus prevails.
Normalization Rationale
All seven parameters are bounded between 0 and 1 for comparability.
Calibration can be based on qualitative coding (expert judgment, historical records) or quantitative proxies (indices of governance, corruption perception, freedom scores).
These parameters are not independent; they interact nonlinearly within the model, shaping coefficients that determine how trust (T), economic stress (E), protest intensity (P), and black horse potential (H) evolve.
By defining leadership in this normalized, multidimensional way, the model transforms leadership qualities from descriptive attributes into mathematical levers. This allows us to formally analyze how leadership alters bifurcation thresholds and the stability of political systems under external shocks.
C. Formal integration of the seven leadership parameters into an ODE system
In this subsection we present a concrete, transparent, and analytically tractable way to embed the seven leadership parameters defined in Section 2.B into a coupled system of ordinary differential equations (ODEs) that governs the time evolution of the state variables (trust), (economic stress), (protest intensity), and (black-horse potential). The presentation below is written to satisfy the precision required for international peer review: every variable and coefficient is defined, assumptions are stated, and the mapping from leadership parameters to model coefficients is explicit.
1. Notation and preliminaries
