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

Kuniyasu SHIMIZU  Tetsuro ENDO  Hisa-Aki TANAKA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.10   pp.2162-2169
Publication Date: 2007/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.10.2162
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Nonlinear Phenomena and Analysis
synchronization,  coupled oscillator system,  averaging method,  nonlinear coupling,  slime amoeba,  

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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.