Solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction

TL;DR

This paper presents an exactly solvable model of a phase oscillator network with Mexican-hat interaction on a circle, deriving self-consistent equations and solutions, and validating findings with simulations.

Contribution

It introduces a new solvable model for phase oscillators with Mexican-hat interaction, providing analytical solutions and frequency distribution insights.

Findings

Three non-trivial solutions characterized by rotation number

Derived self-consistent equations for order parameters

Simulation results closely match theoretical predictions

Abstract

We describe a solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction. We derive self-consistent equations of the order parameters and obtain three non-trivial solutions characterized by the rotation number. We also derive relevant characteristics such as the location-dependent distributions of the resultant frequencies of desynchronized oscillators. Simulation results closely agree with the theoretical ones.