NDLI: On Synchronization of Kuramoto Oscillators

Content Provider	IEEE Xplore Digital Library
Author	Chopra, N. Spong, M.W.
Copyright Year	2005
Description	Author affiliation: Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 W. Main St., Urbana, IL 61801 USA. nchopra@uiuc.edu (Chopra, N.)
Abstract	Synchronization is a key concept to the under-standing of self-organization phenomena occurring in coupled oscillators of the dissipative type. In this paper we study one of the most representative models of coupled phase oscillators, the Kuramoto model. The traditional Kuramoto model (all-to-all connectivity) is said to synchronize if the angular frequencies of all oscillators converge to the mean frequency of the group and the oscillators get phase locked. Recently, Jadbabaie et. al. calculated a lower bound on the coupling gain which is necessary for the onset of synchronization in the traditional Kuramoto model. It was also shown that there exists a large enough coupling gain so that the phase differences are locally asymptotically stable. Furthermore, the authors demonstrated that the convergence is exponential when all oscillators have the same natural frequency. In this paper we assume that the natural frequencies of all oscillators are arbitrarily chosen from the set of reals. We develop a tighter lower bound on the coupling gain, as compared to the one proposed by Jadbabaie et. al., which is necessary for the onset of synchronization in the traditional Kuramoto model. Our main result says that it is possible to find a coupling gain such that the angular frequencies of all oscillators locally exponentially synchronize to the mean frequency of the group. To the best of our knowledge, this is the first result which demonstrates that in the traditional Kuramoto model, with all-to-all coupling and different natural frequencies, the oscillators locally exponentially synchronize.
Starting Page	3916
Ending Page	3922
File Size	174122
Page Count	7
File Format	PDF
ISBN	0780395670
DOI	10.1109/CDC.2005.1582773
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-12-15
Publisher Place	Spain
Access Restriction	Subscribed
Rights Holder	IEEE/EUCA
Subject Keyword	Frequency synchronization Local oscillators Biological system modeling Josephson junctions Convergence Chemicals Chirp Physics Humans Heart beat
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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