The effects of degree distributions in random networks of Type-I neurons

TL;DR

This paper investigates how the width of degree distributions affects the dynamics of large random networks of Type-I neurons, revealing that in-degree broadening impacts oscillations and bistability.

Contribution

It introduces degree-based mean field equations for large theta neuron networks and analyzes the effects of degree distribution widths on network dynamics.

Findings

In-degree broadening destroys oscillations in inhibitory networks.

In-degree broadening decreases bistability in excitatory networks.

Degree distribution variations influence the onset of collective oscillations.

Abstract

We consider large networks of theta neurons and use the Ott/Antonsen ansatz to derive degree-based mean field equations governing the expected dynamics of the networks. Assuming random connectivity we investigate the effects of varying the widths of the in- and out-degree distributions on the dynamics of excitatory or inhibitory synaptically coupled networks, and gap junction coupled networks. For synaptically coupled networks, the dynamics are independent of the out-degree distribution. Broadening the in-degree distribution destroys oscillations in inhibitory networks and decreases the range of bistability in excitatory networks. For gap junction coupled neurons, broadening the degree distribution varies the values of parameters at which there is an onset of collective oscillations. Many of the results are shown to also occur in networks of more realistic neurons.