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 fields. 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 confirm 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 |
Copyright and reproduction |
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) |
Download PDF |
CAS2014-79 NLP2014-73 |
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 |
Keyword(5) |
|
Keyword(6) |
|
Keyword(7) |
|
Keyword(8) |
|
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.) |
6th Author's Name |
|
6th Author's Affiliation |
() |
7th Author's Name |
|
7th Author's Affiliation |
() |
8th Author's Name |
|
8th Author's Affiliation |
() |
9th Author's Name |
|
9th Author's Affiliation |
() |
10th Author's Name |
|
10th Author's Affiliation |
() |
11th Author's Name |
|
11th Author's Affiliation |
() |
12th Author's Name |
|
12th Author's Affiliation |
() |
13th Author's Name |
|
13th Author's Affiliation |
() |
14th Author's Name |
|
14th Author's Affiliation |
() |
15th Author's Name |
|
15th Author's Affiliation |
() |
16th Author's Name |
|
16th Author's Affiliation |
() |
17th Author's Name |
|
17th Author's Affiliation |
() |
18th Author's Name |
|
18th Author's Affiliation |
() |
19th Author's Name |
|
19th Author's Affiliation |
() |
20th Author's Name |
|
20th Author's Affiliation |
() |
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 |
6 |
Date of Issue |
2014-10-09 (CAS, NLP) |
|