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A study about complex motion caused by hierarchical structure and intermittency, in nonlinear dynamical system with large degree of freedom

Research Project

Project/Area Number 12834012
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research InstitutionKagoshima University

Principal Investigator

HATA Hiroki  Kagoshima University, Faculty of Science, Associate Professor, 理学部, 助教授 (30212145)

Co-Investigator(Kenkyū-buntansha) INOUE Masayoshi  Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (80041234)
Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywordshigh dimensional chaos / On-off intermittency / dynamical glass / chaotic itinerancy / anomalous diffusion / Hamilton chaos / generalized shift / volcano / カオス的遍歴現象 / リアプノフ解析 / フラクタル次元
Research Abstract

Various hierarchical structures and motion hide in nonlinear dynamical systems, and so it is an important problem to build new methodology and general idea to understand it. We paid our attention to the hierarchical structure of invariant manifolds in nonlinear dynamical systems with the large degree of freedom as its approach, and understanding the motion theoretically and numerically is our aim of this research.
( i ) To understand the complicated behavior of high dimensional chaos, we began studies invariant manifolds and On-off intermittency around them, already. We developed this study. Then we found that the complex behavior of the large degree of freedom chaos (chaotic itinerancy) is wondering motion between invariant manifolds and shown that we get clear characterization by statistical coarse-graining,
( ii ) The properties of On-off intermittency that is the base of ( i ) had been argued with perturbation theory. We got new knowledge by treating them by non-preservative methods.
… More ( iii ) Many non-chaotic attractors (fixed points, periodic orbits, and quasi-periodic orbits) can exist in a large degree of freedom (the number of attractor suddenly increases with increase of system size). We studied the properties from a viewpoint of response for noise in particular and was found that enough small noise tied attractor and caused intermittent phenomena. In addition, we found what we could describe the motion as anomalous diffusion in macro-quantities of system.
( iv ) We studied also relation intermittency of chaos in conservative dynamical systems and low dimensional invariant structure.
Next to a study about the behavior of dynamical systems mentioned above, we can develop approach for more complicated behavior. We started (a) a characterization of complicated behavior in generalized shift maps by anomalous diffusion, (b) an analysis of EEG pattern by time-series' entropy, (c) an analysis of intermittency of explosions of SAKURAJIMA volcano and (d) a study for the complicated behavior of dynamical systems with the hierarchical structure which seemed to have invariant manifold in an invariant manifold. Less

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] Y.Tsuda, S.Shirouzu, H.Isozaki, H.Sugano, M.Inoue: "Analysis of EEG pattern by time-series entropy"Clinical Neurophysiology. 111. 2339 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Nishi, M.Inoue T.Tanaka, M.Murai: "Analysis of Time Sequences of Explosive Volcanic Eruptions of Sakurajima"Journal of Physical Society of Japan. 70. 1422-1428 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H.Fujisaka, M.Inoue: "Characterization of Various Statistics of Diffusive Motion"Journal of Physical Society of Japan. 70. 2283-2286 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Nishi, A.Setoyama, M.Inoue: "Nonperturbative Analysis of Chaos Synchronization in Coupled Logistic Map"Journal of Physical Society of Japan. 70. 3189-3192 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] R.Ishizaki, H.Shiraishi, M.Kanie, M.Inoue: "Pathological Anomalous Diffusion Diffusion Generated by a Generalized Shift Map"Journal of Physical Society of Japan. 71(3月掲載予定). (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 津田康民, 白水重憲, 菅野久信, 井上政義: "脳波パターンのエントロピー時系列解析"Japanese Journal of Clinical Neurophysiology. 30(8月掲載予定). (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 相澤 洋二, 龍野 正美, 時田 恵一郎, 橋本 敬, 秦 浩起: "複雑さの数理(Complexity : Hierarchical structures and scaling in physics 翻訳)"産業図書. 386 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Tsuda,Y., Shirouzu,S., Isozaki,H., Sugano,H. & Inoue,M.: "Analysis of EEG pattern by time-series entropy"Clinical Neurophysiology. 111. 2339 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nishi,Y., Inoue,M., Tanaka,T. and Murai,M.: "Analysis of Time Sequences of Explosive Volcanic Eruptions of Sakurajima"Journal of Physical Society of Japan. 70. 1422-1428 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Fujisaka,H. and Inoue,M.: "Characterization of Various Statistics of Diffusive Motion"Journal of Physical Society of Japan. 70. 2283-2286 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nishi,Y., Setoyama,A. and Inoue,M.: "Nonperturbative Analysis of Chaos Synchronization in Coupled Logistic Map"Journal of Physical Society of Japan. 70. 3189-3192 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Ishizaki,R., Shiraishi,H., Kanie,M. and Inoue,M.: "Pathological Anomalous Diffusion Generated by a Generalized Shift Map"Journal of Physical Society of Japan. 71. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Tsuda,Y., Shirouzu,S., Sugano,H. & Inoue,M.: "Analysis of EEG pattern by time-series of entropy )in Japanese)"Japanese Journal of Clinical Neurophysiology. 30. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y.Tsuda, S.Shirouzu, H.Isozaki, H.Sugano, M.Inoue: "Analysis of EEG pattern by time-series entropy"Clinical Neurophys isoloogy {\bf 111}, 2339. 111. 2339 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Nishi, M.Inoue, T.Tanaka, M.Murai: "Analysis of Time Sequences of Explosive Volcanic Eruptions of Sakurajima"Journal of Physical Society of Japan. 70. 1422-1428 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Fujisaka, M.Inoue: "Characterization of Various Statistics of Diffusive Motion"Journal of Physical Society of Japan. 70. 2283-2286 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Nishi, A.Setoyama, M.Inoue: "Nonperturbative Analysis of Chaos Synchronization in Coupled Logistic Map"Journal of Physical Society of Japan. 70. 3189-3192 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] R.Ishizaki, H.Shiraishi, M.Kanie, M.Inoue: "Pathological Anomalous Diffusion Diffusion Generated by a Generalized Shift Map"Journal of Physical Society of Japan. 71(3月掲載予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 津田康民, 白水重憲, 菅野久信, 井上政義: "脳波パターンのエントロピー時系列解析"Japanese Journal of Clinical Neurophysiology. 30(8月掲載予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 相澤洋二, 龍野正美, 時田恵一郎, 橋本敬, 秦浩起: "複雑さの数理(Complexity : Hierarchical structures and scaling in physic 翻訳)"産業図書. 386 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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