Gaussian mean-field models of linear systems

Abstract

This paper addresses the issue of modeling meanfield behavior in heterogeneous populations of linear timeinvariant SISO systems. Our analysis is conducted in the frequency domain, where the heterogeneity of input-output mappings (transfer functions) is modeled as a complex-valued Gaussian process. The mean-field model of diffusively coupled agents is obtained as a Gaussian approximation of averaged input-output behavior. It is shown that the strong coupling and the large number of agents reduce the population variance.