Aggregate Fluctuations in Networks With Drift-Diffusion Models Driven by Stable Non-Gaussian Disturbances

Abstract

The focus of this article is to quantify measures of aggregate fluctuations for consensus-seeking networks subject to exogenous noise with $\alpha$ -stable distributions. This type of noise is generated by a class of random measures with heavy-tailed probability distributions. We define a cumulative-scale parameter over the output variables, as a measure of aggregate fluctuation. We show that this class of measures can be characterized implicitly, because finding its explicit form in terms of network parameters is, in general, almost impossible. To this end, we offer several tractable upper bounds in terms of Laplacian spectrum and statistics of the input noise. Our results suggest that relying on Gaussian-based optimal design algorithms will result in nonoptimal solutions for dynamical networks that operate in the face of non-Gaussian noise.