Transitional Dynamics and Quasi-Periodic Solution Observed in Two Asymmetrical Coupled Oscillators

Kuniyasu SHIMIZU  Tetsuro ENDO  Takuya YOSHIMURA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.1   pp.270-278
Publication Date: 2009/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.270
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
Keyword: 
coupled oscillator system,  asymmetrical system,  transitional dynamics,  quasi-periodic solution,  saddle-node bifurcation,  unstable manifold,  

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Summary: 
In this paper, we investigate the transitional dynamics and quasi-periodic solution appearing after the Saddle-Node (SN) bifurcation of a periodic solution in an inductor-coupled asymmetrical van der Pol oscillators with hard-type nonlinearity. In particular, we elucidate, by investigating global bifurcation of unstable manifold (UM) of saddles, that transitional dynamics and quasi-periodic solution after the SN bifurcation appear based on different structure of UM.