A Data-Driven Method to Dissect the Dynamics of the Causal Influence in Complex Dynamical Systems

Abstract

In several natural and physical systems, reconstructing the graph underlying the interactions is fundamental to understand the interplay between units and the mechanisms at the base of their collective behavior. This is the case of coupled networked dynamical systems where due to several environmental and physical factors such as obstacles, sensors limited range, or components failure, the interaction network might vary in time and space. Currently, such dynamics cannot be fully captured by most existing tools nor there exists any available tools to capture these changes in real time. Here, we present a novel method to infer changes in the causal influence of units of a coupled dynamical system. The approach builds on network and information theories to propose a metric evaluating the influence as time evolves of any node on others. The method is validated on self-propelled particles where particles influence status is subject to vary over time. Our proposed method is expected to enrich the toolbox for reconstructing directed interactions in quasi-real time with few data.