System Size Identification from Sinusoidal Probing in Diffusive Complex Networks

TL;DR

This paper introduces a simple, efficient method to determine the size of large, diffusive complex systems by analyzing their response to probing signals, under specific spectral and stability assumptions.

Contribution

It presents a novel approach for system size identification in complex networks using sinusoidal probing, with low computational complexity and specific applicability conditions.

Findings

Method accurately estimates system size under certain spectral conditions.

Approach is computationally efficient and suitable for large systems.

Applicable to relevant real-world complex systems with stability assumptions.

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, diffusively coupled dynamical system, that leverages the response of the system to an injected probing signal. For our method to be applicable, we rely on some assumptions on system's characteristics, namely, on the spectrum of the coupling graph and on the basin stability of its steady state(s). Even though such assumptions imply that our method cannot be applied to any instance of diffusively coupled group of dynamical agents, we argue that it covers relevant and interesting examples. Furthermore, the simplicity of the approach and its low computational complexity renders it very interesting for the systems to which it applies.