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

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.