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Paper Abstract and Keywords
Presentation 2014-01-21 16:40
Bifurcation of 2-Torus and its Covariant Lyapunov Bundle Observed in Coupled Oscillator System
Kyohei Kamiyama (Meiji Univ.), Motomasa Komuro (Teikyo Univ. of Science), Tetsuro Endo (Meiji Univ.) NLP2013-145
Abstract (in Japanese) (See Japanese page) 
(in English) In this paper, we'd like to explain covariant Lyapunov bundle (CLB)
which is generalization of eigen vector for high dimensional torus (2-torus and more).
A coupled oscillator system is given as an example of CLB.
In continuous dynamical system, the CLB is obtained in both flow and Poincare section.
We mainly take up the CLB in Poincare section
because of the interpretative simplicity
for the qualitative change of characteristic of phase space.
Furthermore, in this paper, the computation target of CLB is 2-torus in flow.
2-torus in flow represents 1-torus in Poincare section, this 1-torus is called invariant closed curve (ICC).
A CLB is a set of the covariant Lyapunov vectors (CLV)
which come out from each points of ICC,
and generally, since a set of CLV shapes bundle, we call this CLB.
We demonstrate the 2-torus Neimark-Sacker (2-Torus Neimark-Sacker) bifurcation
in a coupled oscillator system,
and clarify the relationship with asynchronous degeneration.
Keyword (in Japanese) (See Japanese page) 
(in English) covariant Lyapunov bundle / Lyapunov exponent / coupled oscillator system / quasi-periodic solution / Neimark-Sacker bifurcation / asynchronous degeneration / /  
Reference Info. IEICE Tech. Rep., vol. 113, no. 383, NLP2013-145, pp. 89-91, Jan. 2014.
Paper # NLP2013-145 
Date of Issue 2014-01-14 (NLP) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee NLP  
Conference Date 2014-01-21 - 2014-01-22 
Place (in Japanese) (See Japanese page) 
Place (in English) Niseko Park Hotel 
Topics (in Japanese) (See Japanese page) 
Topics (in English) General 
Paper Information
Registration To NLP 
Conference Code 2014-01-NLP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Bifurcation of 2-Torus and its Covariant Lyapunov Bundle Observed in Coupled Oscillator System 
Sub Title (in English)  
Keyword(1) covariant Lyapunov bundle  
Keyword(2) Lyapunov exponent  
Keyword(3) coupled oscillator system  
Keyword(4) quasi-periodic solution  
Keyword(5) Neimark-Sacker bifurcation  
Keyword(6) asynchronous degeneration  
1st Author's Name Kyohei Kamiyama  
1st Author's Affiliation Meiji University (Meiji Univ.)
2nd Author's Name Motomasa Komuro  
2nd Author's Affiliation Teikyo University of Science (Teikyo Univ. of Science)
3rd Author's Name Tetsuro Endo  
3rd Author's Affiliation Meiji University (Meiji Univ.)
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Date Time 2014-01-21 16:40:00 
Presentation Time 20 
Registration for NLP 
Paper # IEICE-NLP2013-145 
Volume (vol) IEICE-113 
Number (no) no.383 
Page pp.89-91 
#Pages IEICE-3 
Date of Issue IEICE-NLP-2014-01-14 

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