  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.
