Bounds and Estimates for the Response to Correlated Fluctuations in Asymmetric Complex Networks

Abstract

We study the spreading of correlated fluctuations through networks with asymmetric and weighted coupling. This can be found in many real systems such as renewable power grids. These systems have so far only been studied numerically. By formulating a network adapted linear response theory, we derive an analytic bound for the response. For colored we find that vulnerability patterns noise are linked to the left Laplacian eigenvectors of the overdamped modes. We show for a broad class of tree-like flow networks, that fluctuations are enhanced in the opposite direction of the flow. This novel mechanism explains vulnerability patterns that were observed in realistic simulations of renewable power grids