System Size Identification from Sinusoidal Probing in Diffusive Complex Networks

Abstract

One of the most fundamental characteristic of a complex system is its size (or volume), which, in many modelling, is represented by the number of its individual components. Complex systems under investigation nowadays are typically large and/or time-varying, rendering their identification challenging. We propose here an accurate and efficient method to determine the size of (i.e., number of agents in) a complex dynamical system. Our only requirement is to be able to inject a probing signal at any point of the system and to measure its response to our probing. The complexity of the approach depends only on the length of the measurements and not on the size of the system investigated, which renders it extremely efficient.