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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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Summary :

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
Publicized
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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