Interplay of inhibition and multiplexing : Largest eigenvalue statistics

TL;DR

This paper explores how inhibition and multiplexing influence the largest eigenvalue statistics of networks, revealing distribution transitions and stability implications through numerical experiments.

Contribution

It uncovers the effects of inhibitory coupling and multiplexing on eigenvalue distributions, highlighting transitions and stability in network systems.

Findings

Presence of inhibition alters eigenvalue behavior in multiplex networks.

Distribution transitions from Weibull to Gumbel or Frechet with multiplexing.

Denser networks tend to converge to Gumbel distribution, indicating higher stability.

Abstract

The largest eigenvalue of a network provides understanding to various dynamical as well as stability properties of the underlying system. We investigate an interplay of inhibition and multiplexing on the largest eigenvalue statistics of networks. Using numerical experiments, we demonstrate that presence of the inhibitory coupling may lead to a very different behaviour of the largest eigenvalue statistics of multiplex networks than those of the isolated networks depending upon network architecture of the individual layer. We demonstrate that there is a transition from the Weibull to the Gumbel or to the Frechet distribution as networks are multiplexed. Furthermore, for denser networks, there is a convergence to the Gumbel distribution as network size increases indicating higher stability of larger systems.