Averaging Method Analysis of Synchronization Characteristics of a Large Number of Nonlinearly Coupled van der Pol Oscillators

Kuniyasu SHIMIZU; Tetsuro ENDO; Hisa-Aki TANAKA

doi:10.1093/ietfec/e90-a.10.2162

Averaging Method Analysis of Synchronization Characteristics of a Large Number of Nonlinearly Coupled van der Pol Oscillators

Kuniyasu SHIMIZU, Tetsuro ENDO, Hisa-Aki TANAKA

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The averaged equation for an arbitrary number of oscillators coupled by nonlinear coupling scheme invented by S. Nagano, is derived. This system is invented as a model of uni-cellular slime amoeba. By using the averaged equation, we investigate the synchronization characteristics of five coupled oscillators and a large number of coupled oscillators. In particular, we present the statistical property of coupled oscillators in terms of coupling factor γ. We also investigate the effect of linear and nonlinear coupling terms for achieving synchronization, and confirm that the nonlinear coupling term plays an important role for strong synchronization than linear coupling term does.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.10 pp.2162-2169

Publication Date: 2007/10/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e90-a.10.2162

Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

Category: Nonlinear Phenomena and Analysis

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Kuniyasu SHIMIZU, Tetsuro ENDO, Hisa-Aki TANAKA, "Averaging Method Analysis of Synchronization Characteristics of a Large Number of Nonlinearly Coupled van der Pol Oscillators" in IEICE TRANSACTIONS on Fundamentals, vol. E90-A, no. 10, pp. 2162-2169, October 2007, doi: 10.1093/ietfec/e90-a.10.2162.
Abstract: The averaged equation for an arbitrary number of oscillators coupled by nonlinear coupling scheme invented by S. Nagano, is derived. This system is invented as a model of uni-cellular slime amoeba. By using the averaged equation, we investigate the synchronization characteristics of five coupled oscillators and a large number of coupled oscillators. In particular, we present the statistical property of coupled oscillators in terms of coupling factor γ. We also investigate the effect of linear and nonlinear coupling terms for achieving synchronization, and confirm that the nonlinear coupling term plays an important role for strong synchronization than linear coupling term does.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.10.2162/_p

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@ARTICLE{e90-a_10_2162,
author={Kuniyasu SHIMIZU, Tetsuro ENDO, Hisa-Aki TANAKA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Averaging Method Analysis of Synchronization Characteristics of a Large Number of Nonlinearly Coupled van der Pol Oscillators},
year={2007},
volume={E90-A},
number={10},
pages={2162-2169},
abstract={The averaged equation for an arbitrary number of oscillators coupled by nonlinear coupling scheme invented by S. Nagano, is derived. This system is invented as a model of uni-cellular slime amoeba. By using the averaged equation, we investigate the synchronization characteristics of five coupled oscillators and a large number of coupled oscillators. In particular, we present the statistical property of coupled oscillators in terms of coupling factor γ. We also investigate the effect of linear and nonlinear coupling terms for achieving synchronization, and confirm that the nonlinear coupling term plays an important role for strong synchronization than linear coupling term does.},
keywords={},
doi={10.1093/ietfec/e90-a.10.2162},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Averaging Method Analysis of Synchronization Characteristics of a Large Number of Nonlinearly Coupled van der Pol Oscillators
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2162
EP - 2169
AU - Kuniyasu SHIMIZU
AU - Tetsuro ENDO
AU - Hisa-Aki TANAKA
PY - 2007
DO - 10.1093/ietfec/e90-a.10.2162
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2007
AB - The averaged equation for an arbitrary number of oscillators coupled by nonlinear coupling scheme invented by S. Nagano, is derived. This system is invented as a model of uni-cellular slime amoeba. By using the averaged equation, we investigate the synchronization characteristics of five coupled oscillators and a large number of coupled oscillators. In particular, we present the statistical property of coupled oscillators in terms of coupling factor γ. We also investigate the effect of linear and nonlinear coupling terms for achieving synchronization, and confirm that the nonlinear coupling term plays an important role for strong synchronization than linear coupling term does.
ER -