Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Time-delayed interactions and synchronization of identical Lohe oscillators


Authors: Sun-Ho Choi and Seung-Yeal Ha
Journal: Quart. Appl. Math. 74 (2016), 297-319
MSC (2010): Primary 92D25, 74A25, 76N10
DOI: https://doi.org/10.1090/qam/1417
Published electronically: March 18, 2016
MathSciNet review: 3505605
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Abstract: We study time-delay effects on the synchronous dynamics of identical Lohe oscillators on the unit sphere. Time delays in the interactions between Lohe oscillators are induced by the finite propagation speed of information or communication, and generate some oscillatory phenomena in the initial time-layer near the initial time. From the viewpoint of synchronization, we provide a sufficient framework for the complete positional synchronization of Lohe oscillators in terms of their initial configuration, time delay, and coupling strength. As long as the time delay is sufficiently small, there is no qualitative effect on synchronization.


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Additional Information

Sun-Ho Choi
Affiliation: Department of Applied Mathematics and the Institute of Natural Sciences, Kyung Hee University, Yongin, 446-701, South Korea
Email: lpgilin@gmail.com

Seung-Yeal Ha
Affiliation: Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, South Korea
Email: syha@snu.ac.kr

DOI: https://doi.org/10.1090/qam/1417
Keywords: Complete positional synchronization, Lyapunov functional approach, Lohe oscillator, time-delay
Received by editor(s): August 17, 2014
Received by editor(s) in revised form: September 21, 2014
Published electronically: March 18, 2016
Additional Notes: The work of the second author was supported by Samsung Science and Technology Foundation under the Project SSTF-BA1401-03. Both authors thank Prof. Marshall Slemrod for the content of Section 4.3
Article copyright: © Copyright 2016 Brown University


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