Critical Points, Stability, and Basins of Attraction of Three Kuramoto Oscillators with Isosceles Triangle Network

TL;DR

This paper analyzes the stability and convergence properties of a Kuramoto oscillator network with three oscillators connected in an isosceles triangle, considering both attractive and repulsive couplings.

Contribution

It provides a complete characterization of critical points, their stability, and a framework for convergence analysis in this specific oscillator network.

Findings

All critical points are classified and their stability conditions are identified.

A framework for studying convergence towards stable critical points is developed.

The analysis includes both attractive and repulsive coupling scenarios.

Abstract

This article investigates the Kuramoto model with three oscillators that are interconnected by an isosceles triangle network. The characteristic of this model is that the coupling connections between the oscillators can be either attractive or repulsive. We list all critical points and investigate their stability. We furthermore present a framework studying convergence towards stable critical points under special coupled strengths. The main tool is the linearization and the monotonicity arguments of oscillator diameter.