Periodic Neural Activity Induced by Network Complexity

TL;DR

This paper investigates how different network topologies, specifically small-world and scale-free networks, can spontaneously induce periodic neural activity, with the phenomenon depending on network size and rewiring probability.

Contribution

It demonstrates that network topology can induce periodic neural activity, contrasting with chaos in regular networks, and characterizes how this depends on network parameters.

Findings

Periodic activity occurs only in small networks.

Higher rewiring probability increases the likelihood of periodic activity.

Period length scales with the square root of network size.

Abstract

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barab\'asi and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with chaotic neural activities exhibited by regular topologies. Periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger. The average length of the periods increases with the square root of the network size.