Global phase-locking in finite populations of phase-coupled oscillators

TL;DR

This paper establishes precise conditions for the existence of fixed points in finite populations of phase-coupled oscillators and derives bounds on the critical coupling strength.

Contribution

It provides new necessary and sufficient conditions for fixed points and bounds on critical coupling in finite oscillator systems.

Findings

Derived exact conditions for fixed points.

Established bounds on critical coupling strength.

Enhanced understanding of phase-locking phenomena.

Abstract

We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.