Using global modeling to unveil hidden couplings in small network motifs

One of the main tasks in network theory is to infer relations among interacting elements. We propose global modeling as a tool to detect links between nodes and their nature. Various situations using small network motifs are investigated under the assumption that the variable to be measured at each node provides full observability when isolated. Such a choice ensures no intrinsic difficulties for getting a global model in the coupled situation. As a first step toward unveiling the coupling function in larger network motifs, we consider three different scenarios involving Rössler systems diffusively coupled, in a couple or embedded in a network, or parametrically forced. We show that the global modeling is able to determine not only the existence of an interaction but also its functional form, to retrieve the dynamics of the whole system, and to extract the equations governing the single node dynamics as if it was isolated.