Analysis of the global structure of chaotic dynamical systems by topological and computational methods

• Project/Area Number: 21540231
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Ryukoku University
• Principal Investigator: OKA Hiroe (KOKUBU Hiroe) 龍谷大学, 理工学部, 教授 (20215221)
• Co-Investigator(Renkei-kenkyūsha): KOKUBU Hiroshi 京都大学, 大学院・理学研究科, 教授 (50202057) ; ARAI Zin 北海道大学, 大学院・理学研究院, 准教授 (80362432)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
• Keywords: 力学系 / 分岐 / カオス / 計算的方法 / Conley指数 / 位相的方法 / 全構造解析 / ネットワーク / 分岐理論

Research Abstract

Using the topological/computational methods which is developed before by the people including me the following study is treated.
1.the improvement of the algorithm of this method for the global structure.
2.mathematical results and consideration obtained by this method concerning the boundary crisis and interior crisis.
3.the application to the data analysis of this method.

Research Products

• [Journal Article] Graph-based topological approximation of saddle-node bifurcatio n in maps (2012)
  • Author(s): Z. Arai, M. Gameiro, T. Gedeon, H. Kokubu, K. Mis chaikow, H. Oka
  • Journal Title: RIMS Bessatsu Volume: (to appear)
  • Peer Reviewed
• [Journal Article] Graph-based topological approximation of saddle-node bifurcation in maps (2012)
  • Author(s): Z.Arai, M.Gameiro, T.Gedeon, H.Kokubu, K.Mischaikow, H.Oka
  • Journal Title: RIMS Bessatsu Volume: (掲載決定)
  • Peer Reviewed
• [Journal Article] Mayer-Vietoris sequences and coverage problems in sensor networks (2011)
  • Author(s): Zin Arai, Kazunori Hayashi and Yasuaki Hiraoka
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 28 Pages: 237-250
  • NAID: 10029520688
  • Peer Reviewed
• [Journal Article] A database schema for the analysis of global dynamics of multi-parameter systems (2009)
  • Author(s): Zin Arai, William Kalies, Hiroshi Kokubu, Konstantin Mischaikow, H. Oka
  • Journal Title: SIAM Journal on Applied Dynamical Systems Volume: 8 Pages: 757-789
  • NAID: 120001629760
  • Peer Reviewed
• [Journal Article] Recent development in rigorous computational methods in dynamical systems (2009)
  • Author(s): Zin Arai, Hiroshi Kokubu, and Pawel Pilarczyk
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 26 Pages: 393-417
  • NAID: 10028169214
  • Peer Reviewed
• [Journal Article] A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems (2009)
  • Author(s): Arai, Kalies, Kokubu, Mischaikow, Oka, Pilarczyk
  • Journal Title: SIAM J.APPLIED DYNAMICAL SYSTEMS c Vol.8, No.3 Pages: 757-789
  • NAID: 120001629760
  • Peer Reviewed
• [Journal Article] Recent development in rigorous computational methods in dynamical systems (2009)
  • Author(s): Arai, Kokubu, Pilarczyk
  • Journal Title: Japan Journal of Industrial and Applied Mathematics 26 Pages: 393-417
  • NAID: 10028169214
  • Peer Reviewed
• [Journal Article] Capturing the global behavior of dynamical systems with Conley-Morse graphs, Advances in Cognitive Neurodynamics(III)
  • Author(s): Z. Arai, H. Kokubu, I. Obayashi
  • Journal Title: Proceedings of The Third International Conference on Cognitive Neurodynamics Volume: (to appear)
  • Peer Reviewed
• [Journal Article] Capturing the global behavior of dynamical systems with Conley-Morse graphs
  • Author(s): Z.Arai, H.Kokubu, I.Obayashi
  • Journal Title: Advances in Cognitive Neurodynamics (III), Proceedings of The Third International Conference on Cognitive Neurodynamics Volume: (掲載決定)
  • Peer Reviewed
• [Presentation] Topological crisis bifurcation (2012)
  • Author(s): Hiroe Oka
  • Organizer: IV Developers Workshop on the Conley-Morse Database Project
  • Place of Presentation: Kauai Beach Resort, Kauai, Hawaii, U. S. A.
• [Presentation] Time series analysis using topological computation method : a preliminary report (2012)
  • Author(s): Hiroshi Kokubu
  • Organizer: ICMC Summer Meeting on Differential Equations
  • Place of Presentation: Brazil
• [Presentation] Topological crisis bifurcation (2012)
  • Author(s): Hiroe Oka
  • Organizer: IV Developers Workshop on the Conley-Morse Database Project
  • Place of Presentation: Kauai, Hawaii, USA(招待講演)
• [Presentation] 力学系の位相計算的方法を用いた分岐問題 (2011)
  • Author(s): 岡宏枝
  • Organizer: 合原最先端数理モデルプロジェクト勉強会
  • Place of Presentation: 東京大学生産技術研究所Cw601
  • Year and Date: 2011-09-10
• [Presentation] Topological-computational methods for analyzing global dynamics and bifurcations (2011)
  • Author(s): Hiroshi Kokubu
  • Organizer: IUTAM Symposium on 50 years of chaos
  • Place of Presentation: Kyoto University, Japan
• [Presentation] Topological computationalapproach to the crisis bifurcations (2011)
  • Author(s): Hiroe Oka
  • Organizer: RIMS Conference on "Frontiers of Topology and Dynamical Systems"
  • Place of Presentation: 京都大学大学院理学研究科数学教室110講義室
• [Presentation] Graph-based topological computation method for global analysis of dynamics and its application to time series analysis (2011)
  • Author(s): Hiroshi Kokubu
  • Organizer: Workshop on Applied Topology
  • Place of Presentation: 博多シティ会議室JR博多駅ビル10F
• [Presentation] A topological-computational approach to the boundary crisis bifurcations (2011)
  • Author(s): Hiroe Oka
  • Organizer: ICIAM2011
  • Place of Presentation: Vancouver, BC, Canada
• [Presentation] Graph based topological computation for global analysis of dynamical systems (2011)
  • Author(s): Hiroshi Kokubu
  • Organizer: Conference on Computational Methods in Dynamics, ICTP
  • Place of Presentation: Trieste, Italy
• [Presentation] Topological computational approach to the crisis bifurcations (2011)
  • Author(s): Hiroe Oka
  • Organizer: RIMS Conference on "Frontiers of Topology and Dynamical Systems"
  • Place of Presentation: 京都大学大学院理学研究科数学教室110講義室(poster)
• [Presentation] Topological-computational methods for analyzing global dynamics and bifurcations (2011)
  • Author(s): Hiroshi Kokubu
  • Organizer: IUTAM Symposium on 50 years of chaos
  • Place of Presentation: Kyoto University(招待講演)
• [Presentation] 力学系の位相的・計算的方法-boundary crisis in the database schema (2010)
  • Author(s): 岡宏枝
  • Organizer: 香川セミナー
  • Place of Presentation: 香川大学教育学部, 3号館
  • Year and Date: 2010-11-20
• [Presentation] 力学系の位相的・計算的方法-boundary crisis in the database schema (2010)
  • Author(s): 岡宏枝
  • Organizer: 香川セミナー
  • Place of Presentation: 香川大学教育学部(香川県)
  • Year and Date: 2010-11-20
• [Presentation] Dynamics of Globally Coupled Maps, Workshop "Computa-tional Homology and Dynamics" (2010)
  • Author(s): Hiroe Oka
  • Organizer: 国際研究集会
  • Place of Presentation: University of Canterbury, Christchurch, New Zeeland
• [Presentation] Dynamics of Globally Coupled Maps (2010)
  • Author(s): Hiroe Oka
  • Organizer: Workshop "Computational Homology and Dynamics"
  • Place of Presentation: Univ.of Canterbury, Christchurch, New Zeeland(招待講演)
• [Presentation] NumericalAnalysis and Scientific Computatuins (2009)
  • Author(s): Hiroshi Kokubu
  • Organizer: Japan-Taiwan Joint Workshop
  • Place of Presentation: National Taiwan Univ.
• [Remarks]
• [Remarks]
  • URL: http://www.math.ryukoku.ac.jp/~oka/
• [Remarks]
  • URL: http://www.math.ryukoku.ac.jp/-oka/