Phase diagram for the Kuramoto model with van Hemmen interactions

TL;DR

This paper analytically derives the phase diagram of a Kuramoto model with van Hemmen interactions, revealing four distinct states depending on coupling parameters, including incoherence and various synchronization patterns.

Contribution

It introduces an analytical phase diagram for a Kuramoto model with quenched van Hemmen interactions, highlighting new synchronization states.

Findings

Four distinct states: incoherence, partial synchronization, partial antiphase synchronization, mixed states.

Analytical phase diagram derived for zero noise and Lorentzian frequency distribution.

System behavior depends on the relative strength of attractive and random couplings.

Abstract

We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a Lorentzian distribution of the oscillators' natural frequencies. Depending on the size of the attractive and random coupling terms, the system displays four states: complete incoherence, partial synchronization, partial antiphase synchronization, and a mix of antiphase and ordinary synchronization.