Mathematical characterization of chaotic itinerancy

• Project/Area Number: 26610034
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Hitotsubashi University
• Principal Investigator: SAIKI YOSHITAKA 一橋大学, 大学院商学研究科, 准教授 (20433740)
• 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.
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥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.

Research Products

• [Int'l Joint Research] University of Maryland/George Mason University/New York University, Courant Institute(米国)
• [Int'l Joint Research] University of Maryland/George Mason University(米国)
• [Int'l Joint Research] INPE/ITA/UnB Gama(ブラジル)
• [Journal Article] Generalized Lorenz Equations on a Three-Sphere (2017)
  • Author(s): Y. Saiki, E. Sander and J. A. Yorke
  • Journal Title: Eurpean Physical Journal Special Topics Volume: 印刷中
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Measuring quasiperiodicity (2016)
  • Author(s): S. Das, C. B. Dock, Y. Saiki, M. Salgado-Flores, E. Sander, J. Wu and J. A. Yorke
  • Journal Title: Europhysics Letters Volume: 114 Pages: 40005-40005
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation (2015)
  • Author(s): Yoshitaka Saiki, Michio Yamada, Abraham C.-L. Chian, Rodrigo A. Miranda and Erico L. Rempel
  • Journal Title: Chaos Volume: 25 Issue: 10 Pages: 103123-103123
  • DOI: 10.1063/1.4933267
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] 複雑現象における同期 (2016)
  • Author(s): 齊木吉隆
  • Organizer: 現象と数理モデル 2016
  • Place of Presentation: 富山第一ホテル（富山県富山市）
  • Year and Date: 2016-12-27
• [Presentation] Weighted Birkhoff Average and Quasiperiodicity (2016)
  • Author(s): Yoshitaka Saiki
  • Organizer: 日本応用数理学会年会 JSIAM-ANZIAM 特別OS
  • Place of Presentation: 北九州国際会議場（福岡県北九州市）
  • Year and Date: 2016-09-13
• [Presentation] 高次元空間における準周期軌道の回転数の計算方法 (2016)
  • Author(s): 齊木吉隆
  • Organizer: RIMS研究集会 力学系とその関連分野の連携探索
  • Place of Presentation: 京都大学数学教室（京都府京都市）
  • Year and Date: 2016-06-09
• [Presentation] 準周期軌道にまつわるバーコフ平均の高速計算とその応用 (2016)
  • Author(s): 齊木吉隆
  • Organizer: 第14回 ダイナミクス研究会中野
  • Place of Presentation: 明治大学中野キャンパス（東京都中野区）
  • Year and Date: 2016-04-16
• [Presentation] Weighted Bihkhoff average and quasiperiodicity (2016)
  • Author(s): 齊木吉隆
  • Organizer: 力学系セミナー
  • Place of Presentation: 北海道大学（北海道・札幌市）
  • Year and Date: 2016-03-22
  • Invited
• [Presentation] Multi-chaos: A Low Dimensional Paradigm for High Dimensional Chaos (2016)
  • Author(s): 齊木吉隆
  • Organizer: 研究集会「現象と数理モデル」
  • Place of Presentation: 姫路キャッスルグランヴィリオホテル（兵庫県・姫路市）
  • Year and Date: 2016-03-08
  • Invited
• [Presentation] Numerical identification of quasiperiodicity (2016)
  • Author(s): 齊木吉隆
  • Organizer: 冬の力学系研究集会
  • Place of Presentation: 日本大学軽井沢研修所（長野県・軽井沢町）
  • Year and Date: 2016-01-10
• [Presentation] 力学系が生み出す準周期軌道の同定手法について (2016)
  • Author(s): 齊木吉隆
  • Organizer: Perspectives in Mathematical Sciences
  • Place of Presentation: 岡山大学（岡山県・岡山市）
  • Year and Date: 2016-01-06
  • Invited
• [Presentation] 多地域景気変動における同期現象 (2015)
  • Author(s): 齊木吉隆
  • Organizer: MIMS共同研究集会「可積分系が拓く現象数理モデル」
  • Place of Presentation: 明治大学（東京都・中野区）
  • Year and Date: 2015-11-06
  • Invited
• [Presentation] 双曲性が崩れた状況における不安定周期軌道展開の試み (2015)
  • Author(s): 齊木吉隆
  • Organizer: 数学協働プログラム研究集会 「大自由度分子系における化学反応機序の理解と制御」
  • Place of Presentation: 北海道大学（北海道・札幌市）
  • Year and Date: 2015-11-01
  • Invited
• [Presentation] Unstable periodic orbits in a coupled intermittent map (2015)
  • Author(s): 齊木吉隆
  • Organizer: RIMS研究集会「ランダム力学系理論とその応用」
  • Place of Presentation: 京都大学（京都府・京都市）
  • Year and Date: 2015-09-30
  • Invited
• [Presentation] 多地域景気変動モデルにおけるカオス的遍歴：数理的側面 (2015)
  • Author(s): 齊木吉隆
  • Organizer: RIMS共同研究「マクロ経済動学の非線形数理」
  • Place of Presentation: 京都大学（京都府・京都市）
  • Year and Date: 2015-09-14
  • Invited
• [Presentation] データ同化手法に関する数理科学的諸相と今後の展望 (2015)
  • Author(s): 齊木吉隆
  • Organizer: 日本応用数理学会
  • Place of Presentation: 金沢大学（石川県・金沢市）
  • Year and Date: 2015-09-10
• [Presentation] Chaotic Itineracy in Regional Business Cycle Synchronization (2015)
  • Author(s): 齊木吉隆
  • Organizer: NED2015
  • Place of Presentation: 中央大学（東京都・八王子市）
  • Year and Date: 2015-06-27
  • Int'l Joint Research
• [Presentation] 非双曲力学系の不安定周期軌道解析 (2014)
  • Author(s): 齊木吉隆
  • Organizer: 関東力学系セミナー
  • Place of Presentation: 東京大学
  • Year and Date: 2014-11-19
  • Invited
• [Presentation] 同期現象の不安定周期軌道解析 (2014)
  • Author(s): 齊木吉隆
  • Organizer: 新潟ミニ研究会
  • Place of Presentation: 新潟大学
  • Year and Date: 2014-04-17 – 2014-04-18
• [Presentation] 同期現象の不安定周期軌道解析 (2014)
  • Author(s): 齊木吉隆
  • Organizer: 金融研究会
  • Place of Presentation: 一橋大学
  • Year and Date: 2014-04-10
  • Invited
• [Remarks]
  • URL: http://www.cm.hit-u.ac.jp/~saiki/paper.html
• [Remarks]
  • URL: http://www.cm.hit-u.ac.jp/~saiki/paper.html
• [Remarks] http://www.cm.hit-u.ac.jp/~saiki/