Capacity-Constrained Instability in Macroeconomic Systems:

Abstract Macroeconomic systems are traditionally analyzed using equilibrium-based frameworks that rely on spectral stability and linear responses to perturbations. However, such approaches fail to capture transient amplification and nonlinear instability mechanisms inherent in non-normal systems. In this work, we develop a capacity-constrained operator-theoretic framework extended by an oscillatory instability formulation. The system is modeled as a non-normal linear operator with additional phase-dependent amplification dynamics. A generalized instability functional is introduced, incorporating both transient growth and nonlinear divergence through oscillatory components. We demonstrate that instability arises when amplified perturbations exceed system capacity, and further show that oscillatory phase mismatch combined with nonlinear amplification leads to finite-time instability, even when classical spectral criteria indicate stability. An empirical proxy for the instability functional is constructed using macro-financial and energy-related indicators. The results indicate that increasing imbalance between system load and adaptive capacity corresponds to rising systemic risk. The proposed framework provides a unified mathematical approach for analyzing instability across economic, financial, and infrastructure systems.