Complex macroscopic behavior in systems of phase oscillators with adaptive coupling

TL;DR

This paper investigates how slow adaptive coupling in large systems of phase oscillators leads to complex behaviors like excitability and intermittency, using dimensionality reduction and analyzing various oscillator models.

Contribution

It introduces a framework for analyzing macroscopic dynamics in adaptive oscillator systems, incorporating time delays, network structure, and frequency distributions.

Findings

Adaptive coupling induces excitability and intermittency.

Robustness of behaviors across different oscillator complexities.

Dimensionality reduction effectively captures macroscopic dynamics.

Abstract

Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a function of either macroscopic or local system properties. For example, we observe macroscopic excitability and intermittent synchrony in a system of time-delayed Kuramoto oscillators with Hebbian and anti-Hebbian learning. We demonstrate the robustness of our findings by considering systems with increasing complexity, including time-delayed oscillators with adaptive network structure and community interaction, as well as a system with bimodally distributed frequencies.