Quantification of the response of coupled dynamical systems

Determine analytical methods that quantify the response of coupled dynamical systems, providing accurate predictions of how these systems respond under networked interactions and perturbations.

Background

The paper studies linearized coupled dynamical systems on networks and investigates how the system’s response changes when the interaction structure is altered, particularly introducing asymmetry and non-normality via a multiplicative structural perturbation. While much of the literature focuses on additive perturbations and symmetric interactions, the authors develop a framework using Baker–Campbell–Hausdorff expansions to approximate averaged local and global responses without relying on eigen-decomposition of potentially defective matrices.

Within this broader context, the authors explicitly note that the general task of quantifying the response of coupled dynamical systems remains an open problem. Their contribution provides partial analytical insight into short-time behavior and the roles of asymmetry and non-normality, but the comprehensive quantification problem is identified as an open challenge in the field.