A virtual space embedding for the analysis of dynamical networks

Networks of dynamical systems are widespread both in nature and in technology applications, but the interplay between the node dynamics, their interconnections and the macroscopic behavior is still not completely understood. In fact, the intrinsically large dimension of the phase space of such networks represents the main obstacle for their analysis and control. In this paper we propose a technique that is based on embedding the network in a (potentially virtual) spatial coordinate system to obtain a simplified description of the overall behavior. We derive conditions under which both the network dynamics and its stability properties can be successfully analyzed using such approach. A network of Fitzhugh-Nagumo systems is used as an illustrative example to show the effectiveness of the proposed technique.