Leadership Parameters and Bifurcation of Political Unrest: A Mathematical Formalism with Case Studies of Soeharto, SBY, Jokowi, and Prabowo
Abstract
This paper develops a mathematical framework to analyze political unrest through the lens of bifurcation theory, integrating leadership parameters with nonlinear dynamic modeling. We propose seven leadership parameters---consensus, legitimacy, crisis management, narrative control, economic stability, elite management, and repression versus consensus---as structural determinants that modulate the coefficients of a coupled differential equation system describing trust (T), economic stress (E), protest intensity (P), and the emergence of alternative leaders (H). By embedding leadership parameters into the formalism, we derive analytical conditions for bifurcation, identify critical thresholds of external economic shocks (_E), and demonstrate how leadership quality shifts these thresholds. Numerical simulations are conducted for four Indonesian leaders---Soeharto, Susilo Bambang Yudhoyono (SBY), Joko Widodo (Jokowi), and Prabowo Subianto---illustrating distinct bifurcation patterns and the potential rise of "black horse" contenders under conditions of low legitimacy and high unrest. The results show that leadership qualities are not only qualitative traits but also mathematical modulators of systemic stability, providing new insights for the study of political dynamics in complex societies.
Main Motivation
Existing mathematical models of unrest focus primarily on external variables (economic shocks, trust erosion, protest contagion).
Leadership quality is usually treated qualitatively, not as a formal parameter in bifurcation analysis.
Our contribution is to synthesize leadership parameters with bifurcation theory, showing mathematically how governance style shifts critical thresholds for unrest and alters the likelihood of black horse emergence.
Indonesia provides an ideal case: four leaders with contrasting leadership profiles (Soeharto, SBY, Jokowi, Prabowo), spanning authoritarian, transitional democratic, and contemporary populist regimes.
Outline
1. Introduction
Background on mathematical modeling of political unrest.