Simulating the phase behavior of the Kuramoto tree

TL;DR

This paper investigates the phase behavior of Kuramoto oscillators on a Y-shaped tree network, revealing transitions between synchronization, wave, and chaos through simulations and heat maps.

Contribution

It introduces a simulation approach for analyzing phase transitions in Kuramoto models on tree networks, focusing on a fundamental Y-shaped structure.

Findings

Identified phase transitions between synchronization, wave, and chaos.

Demonstrated the impact of network size and coupling strength on system behavior.

Provided heat maps illustrating different dynamical states.

Abstract

The Kuramoto model is a versatile mathematical framework that explains phenomena resulting from interactions among phase oscillators. It finds applications in various scientific and engineering domains. In this study, we focused on a Y-shaped network, which serves as the fundamental unit of a tree network. By simulating oscillators on the network, we generated heat maps for different numbers of nodes and coupling strengths and demonstrated the occurrence of different phases. Our findings reveal transitions between synchronization, wave state, and chaos within the system.