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.摘要（Abstract） 现代经济与基础设施系统正承受日益加剧的结构性压力，其典型特征为非线性交互、冲击传播滞后以及容量约束。基于均衡的经典模型无法捕捉由系统负载与容量失衡引发的有限时间不稳定性。 本文构建了一套整合宏观经济动力学（macroeconomic dynamics）、能源系统与战略储备的统一非线性分析框架。文中引入无量纲不稳定性泛函（dimensionless instability functional）以量化系统韧性（system resilience），并建立了稳定性定理（stability theorem），证明当负载超出容量时，系统将在有限时间内发生不稳定性，且该结论与系统的渐近行为无关。 基于该框架对实证信号与结构性观测结果进行解读，并推导出系统层面的相关启示。本研究结果为理解复杂系统的稳定性提供了一致的理论基础。