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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
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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 MSS2022-85 NLP2022-130

Conference Information
Committee NLP MSS  
Conference Date 2023-03-15 - 2023-03-17 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
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Paper Information
Registration To NLP 
Conference Code 2023-03-NLP-MSS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Study on Properties of Koopman Eigenfunctions for a Planar Singularly-Perturbed Dynamical System 
Sub Title (in English)  
Keyword(1) Koopman operator  
Keyword(2) singularly-perturbed dynamical system  
Keyword(3) global properties of a flow  
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1st Author's Name Natsuki Katayama  
1st Author's Affiliation Kyoto University (Kyoto Univ.)
2nd Author's Name Yoshihiko Susuki  
2nd Author's Affiliation 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
Date of Issue 2023-03-08 (MSS, NLP) 


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