Interplay of inhibition and multiplexing: Largest eigenvalue statistics

¹ Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore - Simrol, Indore-453552, India
² Department of Applied Mathematics, Lobachevsky State University of Nizhny - Novgorod, Russia

^(a) sarikajalan9@gmail.com (corresponding author)

Received: 9 March 2016
Accepted: 24 June 2016

Abstract

The largest eigenvalue of a network provides understanding to various dynamical as well as stability properties of the underlying system. We investigate the interplay of inhibition and multiplexing on the largest eigenvalue statistics of networks. Using numerical experiments, we demonstrate that the presence of the inhibitory coupling may lead to a behaviour of the largest eigenvalue statistics of multiplex networks very different from that of isolated networks depending upon the network architecture of the individual layer. We demonstrate that there is a transition from the Weibull to the Gumbel or to the Fréchet 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.