Paper Abstract and Keywords |
Presentation |
2023-03-16 11:40
A Study on Properties of Koopman Eigenfunctions for a Planar Singularly-Perturbed Dynamical System Natsuki Katayama, Yoshihiko Susuki (Kyoto Univ.) MSS2022-85 NLP2022-130 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The Koopman operator is a composition operator for nonlinear dynamical systems. The eigenfunctions of the Koopman operator, called Koopman eigenfunctions, capture the global properties of flows. In this report, we introduce the Koopman operator to a planar singularly-perturbed dynamical system with an asymptotically stable limit cycle and compute two Koopman eigenfunctions associated with two eigenvalues, the fundamental frequency and the characteristic exponent of the limit cycle. In this system, we introduce multiple manifolds along the nullcline corresponding to the fast variable and show that the Koopman eigenfunction associated with the fundamental frequency becomes steep on these manifolds. A novel method to compute another Koopman eigenfunction is presented by introducing a variational system on a limit cycle. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Koopman operator / singularly-perturbed dynamical system / global properties of a flow / / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 122, no. 436, NLP2022-130, pp. 114-119, March 2023. |
Paper # |
NLP2022-130 |
Date of Issue |
2023-03-08 (MSS, NLP) |
ISSN |
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) |
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MSS2022-85 NLP2022-130 |
Conference Information |
Committee |
NLP MSS |
Conference Date |
2023-03-15 - 2023-03-17 |
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(See Japanese page) |
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Registration To |
NLP |
Conference Code |
2023-03-NLP-MSS |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
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(See Japanese page) |
Title (in English) |
A Study on Properties of Koopman Eigenfunctions for a Planar Singularly-Perturbed Dynamical System |
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Koopman operator |
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singularly-perturbed dynamical system |
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global properties of a flow |
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1st Author's Name |
Natsuki Katayama |
1st Author's Affiliation |
Kyoto University (Kyoto Univ.) |
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Yoshihiko Susuki |
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Kyoto University (Kyoto Univ.) |
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Speaker |
Author-1 |
Date Time |
2023-03-16 11:40:00 |
Presentation Time |
20 minutes |
Registration for |
NLP |
Paper # |
MSS2022-85, NLP2022-130 |
Volume (vol) |
vol.122 |
Number (no) |
no.435(MSS), no.436(NLP) |
Page |
pp.114-119 |
#Pages |
6 |
Date of Issue |
2023-03-08 (MSS, NLP) |
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