Synchronization of Coupled Kuramoto Oscillators under Resource Constraints*

A fundamental understanding of synchronized behavior in multi-agent systems can be acquired by studying analytically tractable Kuramoto models. Yet, such models typically diverge from many real systems whose dynamics evolve under marked resource constraints. Here we construct a system of coupled Kuramoto oscillators that consume or produce resources as a function of their oscillation frequency. At high coupling, we observe strongly synchronized dynamics, whereas at low coupling, we observe independent oscillator dynamics, as expected. For intermediate coupling which typically induces a partially synchronized state, we demonstrate that the system can exist in either an oscillatory synchronization state or a bistable synchronization state depending on whether the oscillators consume or produce resources, respectively. Relevant for systems as varied as coupled neurons and social groups, our study lays important groundwork for future efforts developing quantitative predictions of synchronized dynamics for systems embedded in environments marked by resource constraints.