Improved numerical scheme for the generalized Kuramoto model
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Published:2023-04-01
Issue:4
Volume:2023
Page:043403
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ISSN:1742-5468
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Container-title:Journal of Statistical Mechanics: Theory and Experiment
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language:
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Short-container-title:J. Stat. Mech.
Author:
Keun Lee Hyun,Hong Hyunsuk,Yeo Joonhyun
Abstract
Abstract
We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the generalized Kuramoto model corresponds to particles on the unit sphere undergoing rigid body rotations with position-dependent angular velocities. We demonstrate that our improved scheme is able to reproduce known analytic results and capture the expected behavior of the three-dimensional oscillators in various cases. On the other hand, we find that the conventional numerical method, which amounts to a direct numerical integration with the constraint that forces the particles to be on the unit sphere at each time step, may result in inaccurate and misleading behavior especially in the long time limit. We analyze in detail the origin of the discrepancy between the two methods and present the effectiveness of our method in studying the limit cycle of the Kuramoto oscillators.
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
1 articles.
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