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Paper Abstract and Keywords
Presentation 2014-10-17 13:40
Numerical sensitivity of the derivation of Lyapunov diagram in a discrete-time dynamical system generating invariant three-torus
Shuya Hidaka, Naohiko Inaba, Kyohei Kamiyama (Meiji Univ.), Munehisa Sekikawa (Utsunomiya Univ.), Tetsuro Endo (Meiji Univ.) CAS2014-79 NLP2014-73
Abstract (in Japanese) (See Japanese page) 
(in English) In this study, we investigate quasi-periodic bifurcations in a three-coupled delayed logistic map that generates an invariant three-torus (IT3). Here, IT3 in this map corresponds to a four-torus in vector fi elds. First, to obtain a clear Lyapunov diagrams for two-frequency, three-frequency, and four-frequency quasi-periodic oscillations, we demonstrate that it is important that the number of iterations deleted as a transient state is large.For example, it is necessary to delete 10,000,000 transient iterations as well as 10,000,000 stationary state iterations to evaluate Lyapunov exponents in this higher-dimensional discrete-time dynamical system. Second, by observing the graph of Lyapunov exponents, the global transition from an invariant two-torus (IT2) to an IT3 could be a one-dimension-higher quasi-periodic Hopf (or quasi-periodic Neimark-Sacker) bifurcation of an IT2. In addition, we con firm that another bifurcation route from an IT2 to an IT3 could be caused by a one-dimension-higher quasi-periodic saddle-node bifurcation of an IT2.
Keyword (in Japanese) (See Japanese page) 
(in English) invariant three-torus / bifurcations / delayed logistic map / Lyapunov diagram / / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 250, NLP2014-73, pp. 139-144, Oct. 2014.
Paper # NLP2014-73 
Date of Issue 2014-10-09 (CAS, NLP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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Conference Information
Committee NLP CAS  
Conference Date 2014-10-16 - 2014-10-17 
Place (in Japanese) (See Japanese page) 
Place (in English) Ehime University 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Nonlinear Problems, etc. 
Paper Information
Registration To NLP 
Conference Code 2014-10-NLP-CAS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Numerical sensitivity of the derivation of Lyapunov diagram in a discrete-time dynamical system generating invariant three-torus 
Sub Title (in English)  
Keyword(1) invariant three-torus  
Keyword(2) bifurcations  
Keyword(3) delayed logistic map  
Keyword(4) Lyapunov diagram  
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1st Author's Name Shuya Hidaka  
1st Author's Affiliation Meiji University (Meiji Univ.)
2nd Author's Name Naohiko Inaba  
2nd Author's Affiliation Meiji University (Meiji Univ.)
3rd Author's Name Kyohei Kamiyama  
3rd Author's Affiliation Meiji University (Meiji Univ.)
4th Author's Name Munehisa Sekikawa  
4th Author's Affiliation Utsunomiya University (Utsunomiya Univ.)
5th Author's Name Tetsuro Endo  
5th Author's Affiliation Meiji University (Meiji Univ.)
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Speaker Author-1 
Date Time 2014-10-17 13:40:00 
Presentation Time 20 minutes 
Registration for NLP 
Paper # CAS2014-79, NLP2014-73 
Volume (vol) vol.114 
Number (no) no.249(CAS), no.250(NLP) 
Page pp.139-144 
#Pages
Date of Issue 2014-10-09 (CAS, NLP) 


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