Triadic State Space in Non-Normal Dynamics: A Phase Classification Based on the K-Functional"

Abstract We introduce a triadic phase classification for non-normal dynamical systems based on the K-functional and its logarithmic growth rate. While classical theory distinguishes between stable and unstable regimes, we show that a three-phase structure naturally emerges when transient amplification and its dynamics are taken into account. The framework defines three regimes—stable, transitional, and supercritical—based on the magnitude of the K-functional and its growth rate. These regimes provide a mathematically consistent classification of system behavior and offer a unified interpretation of stability, amplification, and collapse in non-normal systems.