Asymptotic Frequency Synchronization of Kuramoto Model by Step Force

2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yanbing Mao ◽  
Ziang Zhang
Keyword(s):  
Kuramoto Model ◽  
Frequency Synchronization

Remarks on the complete synchronization for the Kuramoto model with frustrations

2018 ◽  
Vol 16 (04) ◽  
pp. 525-563 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Hwa Kil Kim ◽  
Jinyeong Park
Keyword(s):  
Phase Synchronization ◽  
Kuramoto Model ◽  
Prototype Model ◽  
Frequency Synchronization ◽  
Complete Synchronization ◽  
Synchronization Problem ◽  
Kuramoto Oscillators ◽  
Applicable Range ◽  
The Kuramoto Model ◽  
Complete Frequency

The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity 28 (2015) 1441–1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci. 26 (2016) 357–382.] which can be applicable only for initial configurations confined in a half circle.

scholarly journals Approximate solution for frequency synchronization in a finite-size Kuramoto model

2015 ◽  
Vol 92 (6) ◽  
Author(s):  
Chengwei Wang ◽  
Nicolás Rubido ◽  
Celso Grebogi ◽  
Murilo S. Baptista
Keyword(s):  
Approximate Solution ◽  
Finite Size ◽  
Kuramoto Model ◽  
Frequency Synchronization

scholarly journals Nontrivial standing wave state in frequency-weighted Kuramoto model

2017 ◽  
Vol 12 (3) ◽  
Author(s):  
Hong-Jie Bi ◽  
Yan Li ◽  
Li Zhou ◽  
Shu-Guang Guan
Keyword(s):  
Standing Wave ◽  
Kuramoto Model ◽  
Wave State

scholarly journals Emulating the local Kuramoto model with an injection-locked photonic crystal laser array

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Naotomo Takemura ◽  
Kenta Takata ◽  
Masato Takiguchi ◽  
Masaya Notomi
Keyword(s):  
Photonic Crystal ◽  
Nearest Neighbor ◽  
Multiple Quantum Well ◽  
Kuramoto Model ◽  
Multiple Quantum ◽  
Laser Array ◽  
Novel Strategy ◽  
A Chain ◽  
The One ◽  
The Kuramoto Model

AbstractThe Kuramoto model is a mathematical model for describing the collective synchronization phenomena of coupled oscillators. We theoretically demonstrate that an array of coupled photonic crystal lasers emulates the Kuramoto model with non-delayed nearest-neighbor coupling (the local Kuramoto model). Our novel strategy employs indirect coupling between lasers via additional cold cavities. By installing cold cavities between laser cavities, we avoid the strong coupling of lasers and realize ideal mutual injection-locking with effective non-delayed dissipative coupling. First, after discussing the limit cycle interpretation of laser oscillation, we demonstrate the synchronization of two indirectly coupled lasers by numerically simulating coupled-mode equations. Second, by performing a phase reduction analysis, we show that laser dynamics in the proposed device can be mapped to the local Kuramoto model. Finally, we briefly demonstrate that a chain of indirectly coupled photonic crystal lasers actually emulates the one-dimensional local Kuramoto chain. We also argue that our proposed structure, which consists of periodically aligned cold cavities and laser cavities, will best be realized by using state-of-the-art buried multiple quantum well photonic crystals.

scholarly journals Frequency synchronization detection method based on adaptive frequency standard tracking

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 434-438
Author(s):  
Xin Geng ◽  
Baoqiang Du ◽  
Jianwei Zhang ◽  
Erlin Tian
Keyword(s):  
Detection Method ◽  
Wide Band ◽  
Frequency Standard ◽  
Frequency Measurement ◽  
Measurement Range ◽  
Period Change ◽  
Measured Signal ◽  
Frequency Synchronization ◽  
Measured Frequency ◽  
Field Programmable

Abstract In order to achieve wide-band high-resolution frequency measurement, a frequency synchronization detection method based on adaptive frequency standard tracking is proposed based on the quantized phase processing. First, the nominal value of the measured frequency signal was obtained from the rough frequency measurement module. Then, the field programmable gate array generated the nominal value of the measured frequency. After that, the direct comparison between the tracking frequency and the measured signal was carried out. Finally, the group quantized processing module gave the final result according to the phase full-period change time. Experimental results showed that the method has a wide frequency measurement range and high accuracy and can obtain frequency stability of the order of 10−13/s.

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