Instability in Networked Systems: A Non-Normal Amplification Framework"

Abstract We investigate instability mechanisms in networked dynamical systems through the lens of non-normal operator theory. While classical network analysis emphasizes topology and spectral properties, we demonstrate that transient amplification induced by non-normal coupling plays a central role in systemic instability. We introduce a network-based formulation of the K-functional that incorporates structural connectivity and effective interaction complexity. The framework establishes conditions under which perturbations propagate and amplify across networks, leading to cascade effects even in spectrally stable systems.