Mathematical characterization of chaotic itinerancy
Project/Area Number |
26610034
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Foundations of mathematics/Applied mathematics
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Research Institution | Hitotsubashi University |
Principal Investigator |
SAIKI YOSHITAKA 一橋大学, 大学院商学研究科, 准教授 (20433740)
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Research Collaborator |
ESASHI Kunihiko
ONOZAKI Tamotsu
KOBAYASHI Miki U
SATO Yuzuru
YAMADA Michio
Chian Abraham C.-L.
Das Suddhasattwa
Dock Chris B.
Miranda Rodrigo A.
Salgado-Flores Martin
Rempel Erico L.
Sander Evelyn
Wu Jin
Yorke James A.
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Project Period (FY) |
2014-04-01 – 2017-03-31
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Project Status |
Completed (Fiscal Year 2016)
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Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 力学系 / 数値解析 / 応用数学 / 複雑現象の数理 / 大規模数値解析 / カオス / 不安定周期軌道 / カオス的遍歴 / 準周期軌道 / 非双曲性 / 間欠性 |
Outline of Final Research Achievements |
Chaotic itinerancy is know as "Complex phenomena wandering among multi chaotic states irregularly", but does not have a certain mathematical characterization. We analyze a dynamics of a minimal model having the inevitable properties to be chaotic itinerancy. One of the models we studied was a two-dimensional torus map showing intermittency. It is expanding in x-direction and expanding or contracting in y-direction depending on the x value. We find that behind the dynamics exist the coexistence of repellers and saddles and quasi-periodic orbits. Through this study we develop a technique for calculating the Birkhoff average along a quasiperiodic orbit.
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Report
(4 results)
Research Products
(26 results)
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[Journal Article] Measuring quasiperiodicity2016
Author(s)
S. Das, C. B. Dock, Y. Saiki, M. Salgado-Flores, E. Sander, J. Wu and J. A. Yorke
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Journal Title
Europhysics Letters
Volume: 114
Pages: 40005-40005
Related Report
Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
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