Critical points, stability, and basins of attraction of three Kuramoto oscillators with isosceles triangle network

Xiaoxue ZHAO; Xiang ZHOU

doi:10.1016/j.aml.2024.109246

Critical points, stability, and basins of attraction of three Kuramoto oscillators with isosceles triangle network

Xiaoxue ZHAO, Xiang ZHOU^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

We investigate the Kuramoto model with three oscillators 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.© 2024 Elsevier Ltd.

Original language	English
Article number	109246
Number of pages	6
Journal	Applied Mathematics Letters
Volume	158
Online published	27 Jul 2024
DOIs	https://doi.org/10.1016/j.aml.2024.109246
Publication status	Published - Dec 2024

Funding

This work is partially supported by Hong Kong RGC GRF grants 11308121 , 11318522 and 11308323 . Zhao acknowledges the supported of the Hong Kong Scholars Scheme (Grant No. XJ2023001 ), the National Natural Science Foundation of China (Grant No. 12201156 ), the China Postdoctoral Science Foundation, China (Grant No. 2021M701013 ). We thank Peng Zhang at City University of Hong Kong for introducing us the background of flame oscillation.

Research Keywords

Kuramoto model
Critical point
Stability
Basin of attraction

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title = "Critical points, stability, and basins of attraction of three Kuramoto oscillators with isosceles triangle network",

abstract = "We investigate the Kuramoto model with three oscillators 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.{\textcopyright} 2024 Elsevier Ltd.",

keywords = "Kuramoto model, Critical point, Stability, Basin of attraction",

author = "Xiaoxue ZHAO and Xiang ZHOU",

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language = "English",

volume = "158",

journal = "Applied Mathematics Letters",

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TY - JOUR

T1 - Critical points, stability, and basins of attraction of three Kuramoto oscillators with isosceles triangle network

AU - ZHAO, Xiaoxue

AU - ZHOU, Xiang

PY - 2024/12

Y1 - 2024/12

N2 - We investigate the Kuramoto model with three oscillators 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.© 2024 Elsevier Ltd.

AB - We investigate the Kuramoto model with three oscillators 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.© 2024 Elsevier Ltd.

KW - Kuramoto model

KW - Critical point

KW - Stability

KW - Basin of attraction

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85199949400&origin=recordpage

U2 - 10.1016/j.aml.2024.109246

DO - 10.1016/j.aml.2024.109246

M3 - RGC 21 - Publication in refereed journal

SN - 0893-9659

VL - 158

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 109246

ER -

Critical points, stability, and basins of attraction of three Kuramoto oscillators with isosceles triangle network

Abstract

Funding

Research Keywords

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GRF: Machine-Learning-based String Method for Minimum Energy Path in Probability Measure Space

GRF: Topics on Dynamics and Algorithms for Saddle Point Calculation

GRF: Theory of Deep Learning: from CNNs to RNNs

Cite this

Critical points, stability, and basins of attraction of three Kuramoto oscillators with isosceles triangle network

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: Machine-Learning-based String Method for Minimum Energy Path in Probability Measure Space

GRF: Topics on Dynamics and Algorithms for Saddle Point Calculation

GRF: Theory of Deep Learning: from CNNs to RNNs

Cite this