Stability of Energy Systems under Price Shocks: A Non-Normal Operator Approach

Abstract Energy systems are a central component of modern macroeconomic stability, yet they are increasingly exposed to volatility driven by fossil fuel price fluctuations. Classical models treat such shocks as exogenous disturbances within equilibrium frameworks, assuming that systems return to stability over time. In this work, energy-dependent economic systems are modeled as non-normal dynamical systems subject to capacity constraints. It is shown that energy price shocks can induce significant transient amplification, leading to instability even when spectral conditions suggest stability. A dimensionless functional is introduced to quantify the interaction between amplification and system capacity. The analysis demonstrates that dependence on volatile energy inputs increases system non-normality and reduces stability margins. Numerical simulations illustrate how energy shocks propagate through interconnected systems, producing amplification effects that may exceed capacity limits. The results provide a mathematical framework for understanding energy-driven instability and highlight the stabilizing role of structural energy transitions.