Nonlinear Capacity and System Stability: A Unified Framework for Macroeconomic, Energy, and Strategic Reserve Systems

Abstract Modern economic and infrastructure systems operate under increasing structural stress characterized by nonlinear interactions, delayed shock propagation, and capacity constraints. Classical equilibrium-based models fail to capture finite-time instability arising from the imbalance between system load and capacity. This paper develops a unified nonlinear framework integrating macroeconomic dynamics, energy systems, and strategic reserves. A dimensionless instability functional is introduced to quantify system resilience. A stability theorem is established, demonstrating that instability occurs in finite time when load exceeds capacity, independently of asymptotic behavior. Empirical signals and structural observations are interpreted within this framework, and system-level implications are derived. The results provide a consistent theoretical foundation for understanding stability in complex systems.