Chaotic synchronization in adaptive networks of pulse-coupled oscillators

TL;DR

This paper demonstrates that a mean-field model of pulse-coupled oscillators with adaptive coupling can produce robust irregular synchronized dynamics, mimicking neural networks with excitatory and inhibitory neurons.

Contribution

It introduces a simple mean-field model with adaptive coupling and phase-response shaping that captures complex neural-like synchronization phenomena.

Findings

Strongly synchronized irregular regimes observed

Homeostatic mechanism stabilizes synchronization

Model mimics neural network dynamics

Abstract

Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a robust irregular macroscopic dynamics. The resulting, strongly synchronized, regime is sustained by a homeostatic mechanism induced by the shape of the phase-response curve combined with adaptive coupling strength, included to account for energy dissipated by the pulse emission. The proposed setup mimicks a neural network composed of excitatory and inhibitory neurons.