Inhibition as a determinant of activity and criticality in dynamical networks

TL;DR

This paper investigates how inhibition influences activity and criticality in dynamical networks, revealing that inhibition strength, rather than degree, governs network sensitivity and criticality, with implications for adaptive network design.

Contribution

It introduces a mean-field framework for understanding inhibition's role in network dynamics and demonstrates robustness of activity against topological changes.

Findings

Inhibition strength determines network criticality and sensitivity.

Degree K's influence diminishes at high connectivity levels.

Adaptive threshold networks maintain dynamics despite topological variations.

Abstract

A certain degree of inhibition is a common trait of dynamical networks in nature, ranging from neuronal and biochemical networks, to social and technological networks. We study here the role of inhibition in a representative dynamical network model, characterizing the dynamics of random threshold networks with both excitatory and inhibitory links. Varying the fraction of excitatory links has a strong effect on the network's population activity and its sensitivity to perturbation. The average degree $K$, known to have a strong effect on the dynamics when small, loses its influence on the dynamics as its value increases. Instead, the strength of inhibition is a determinant of dynamics and sensitivity here, allowing for criticality only in a specific corridor of inhibition. This criticality corridor requires that excitation dominates, while the balance region corresponds to maximum sensitivity to perturbation. We develop mean-field approximations of the population activity and sensitivity and find that the network dynamics is independent of degree distribution for high $K$. In a minimal model of an adaptive threshold network we demonstrate how the dynamics remains robust against changes in the topology. This adaptive model can be extended in order to generate networks with a controllable activity distribution and specific topologies.