Self-Sustaining Oscillations in Complex Networks of Excitable Elements

TL;DR

This paper investigates how random networks of excitable elements can self-organize into sustained oscillations through loop structures, with implications for understanding phenomena like epileptic seizures.

Contribution

It reveals the mechanism of self-sustaining oscillations in complex networks and identifies the role of network loops and initial conditions in this process.

Findings

Oscillations arise in networks with loops and random initial conditions.

Specific loops act as pacemakers driving the oscillations.

The mechanism may be relevant to epileptic seizures.

Abstract

Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently random. In the oscillating state, signals propagate in a single direction and one or a few network loops are selected as driving loops in which the excitation circulates periodically. We analyze the mechanism, describe the oscillating states, identify the pacemaker loops and explain key features of their distribution. This mechanism may play a role in epileptic seizures.