On synchronization of coupled Hopf-Kuramoto oscillators with phase delays

Soon Jo Chung; Jean Jacques Slotine

doi:10.1109/CDC.2010.5717962

On synchronization of coupled Hopf-Kuramoto oscillators with phase delays

Soon Jo Chung, Jean Jacques Slotine

Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper presents new methods and results on synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any positive coupling gain is proven to induce almost global asymptotic synchronization, and a threshold value for truly global exponential synchronization is also computed. Furthermore, a hierarchical connection between coupled Hopf oscillators and Kuramoto oscillators is identified. Finally, a new result on the synchronization of Kuramoto oscillators with arbitrary time-varying heterogeneous frequencies and delays is derived.

Original language	English (US)
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3181-3187
Number of pages	7
ISBN (Print)	9781424477456
DOIs	https://doi.org/10.1109/CDC.2010.5717962
State	Published - 2010
Event	49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States Duration: Dec 15 2010 → Dec 17 2010

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	49th IEEE Conference on Decision and Control, CDC 2010
Country/Territory	United States
City	Atlanta
Period	12/15/10 → 12/17/10

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Online availability

10.1109/CDC.2010.5717962

Library availability

Discover UIUC Full Text

Cite this

On synchronization of coupled Hopf-Kuramoto oscillators with phase delays. / Chung, Soon Jo; Slotine, Jean Jacques.
2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc., 2010. p. 3181-3187 5717962 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Chung, SJ & Slotine, JJ 2010, On synchronization of coupled Hopf-Kuramoto oscillators with phase delays. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717962, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 3181-3187, 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717962

@inproceedings{e0bc1a36227846d3ab3f51f9ee919fc8,

title = "On synchronization of coupled Hopf-Kuramoto oscillators with phase delays",

abstract = "This paper presents new methods and results on synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any positive coupling gain is proven to induce almost global asymptotic synchronization, and a threshold value for truly global exponential synchronization is also computed. Furthermore, a hierarchical connection between coupled Hopf oscillators and Kuramoto oscillators is identified. Finally, a new result on the synchronization of Kuramoto oscillators with arbitrary time-varying heterogeneous frequencies and delays is derived.",

author = "Chung, {Soon Jo} and Slotine, {Jean Jacques}",

year = "2010",

doi = "10.1109/CDC.2010.5717962",

language = "English (US)",

isbn = "9781424477456",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "3181--3187",

booktitle = "2010 49th IEEE Conference on Decision and Control, CDC 2010",

address = "United States",

note = "49th IEEE Conference on Decision and Control, CDC 2010 ; Conference date: 15-12-2010 Through 17-12-2010",

}

TY - GEN

T1 - On synchronization of coupled Hopf-Kuramoto oscillators with phase delays

AU - Chung, Soon Jo

AU - Slotine, Jean Jacques

PY - 2010

Y1 - 2010

N2 - This paper presents new methods and results on synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any positive coupling gain is proven to induce almost global asymptotic synchronization, and a threshold value for truly global exponential synchronization is also computed. Furthermore, a hierarchical connection between coupled Hopf oscillators and Kuramoto oscillators is identified. Finally, a new result on the synchronization of Kuramoto oscillators with arbitrary time-varying heterogeneous frequencies and delays is derived.

AB - This paper presents new methods and results on synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any positive coupling gain is proven to induce almost global asymptotic synchronization, and a threshold value for truly global exponential synchronization is also computed. Furthermore, a hierarchical connection between coupled Hopf oscillators and Kuramoto oscillators is identified. Finally, a new result on the synchronization of Kuramoto oscillators with arbitrary time-varying heterogeneous frequencies and delays is derived.

UR - http://www.scopus.com/inward/record.url?scp=79953129813&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953129813&partnerID=8YFLogxK

U2 - 10.1109/CDC.2010.5717962

DO - 10.1109/CDC.2010.5717962

M3 - Conference contribution

AN - SCOPUS:79953129813

SN - 9781424477456

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3181

EP - 3187

BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 49th IEEE Conference on Decision and Control, CDC 2010

Y2 - 15 December 2010 through 17 December 2010

ER -

On synchronization of coupled Hopf-Kuramoto oscillators with phase delays

Abstract

Publication series

Conference

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this