Predicting the response of structurally altered and asymmetrical networks

We investigate how the response of coupled dynamical systems is modified due to a structural alteration of the interaction. The majority of the literature focuses on additive perturbations and symmetrical interaction networks. Here, we consider the challenging problem of multiplicative perturbations and asymmetrical interaction coupling. We introduce a framework to approximate the averaged response at each network node for general structural perturbations, including non-normal and asymmetrical ones. Our findings indicate that both the asymmetry and non-normality of the structural perturbation impact the global and local responses at different orders in time. We propose a set of matrices to identify the nodes whose response is affected the most by the structural alteration.