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Study of Response, Propagation, and Reconstruction of High-dimensional Chaos with Coupled Maps

Research Project

Project/Area Number 05836006
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 非線形科学
Research InstitutionThe University of Tokyo

Principal Investigator

KANEKO Kunihiko  The University of Tokyo, colloege of Arts and Sciences, Professor, 教養学部, 教授 (30177513)

Project Period (FY) 1993 – 1994
Project Status Completed (Fiscal Year 1994)
Budget Amount *help
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1994: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1993: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsChaos / Turbulence / High-dimensional Chaos / Spatiotemporal Chaos / Clustering / Biological Information Processing / Coupled Map Lattice / クラスター / ひきこみ / ハミルトン力学系 / 空間カオス
Research Abstract

We have studied features of high-dimensional chaos, including spatiotemporal chaos by means of coupled map lattices (CML). In particular we have clarified the following features.
1.The pattern dynamics of the open-flow CML is studied. Spatial chaos with temporal periodicity is found, whose stability is analyzed by the co-moving Lyapunov exponents. Organization of periodic lattice of chaotic defects is found, whose mechanism is explained by the dynamical systems theory, while intermittent transition of such defects is found in stronger nonlinearity.
2.Selection of attractors and amplified propagation of periodic inputs are studied in the open flow model. The study leads to the controalbility of patterns by tiny inputs. Possible applications to information processings are discussed.
3.Two types of ordered states, clustered and dispersed states are found in Hamiltonian system with attractive and repulsive forces respectively. A variety of ordered states coexist depednding on initial conditions, which form onion structures in the phase space. This discovery gives a novel mechanism of order formation in many-particle systems.
4.CML for Benard convection is analyzed, which reproduces all known phenomena in experiments and leads to several novel predictions on turbulent behaviors and chaotic itinerancy.
5.The cascade information flow is found in globally coupled maps, while the chaotic itinerancy and dynamics of relationships between elements are studied in a variety of coupled map systems. Their relevenace to biological information prcoessings are discussed.

Report

(3 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] K.Kaneko and T.Konishi: "Peeling the Onion of Order and Chaos in a High-dimensional Hamiltonian System" Physica D. 71. 146-167 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko: "Relevance of Clustering to Biological Networks." Physica D. 75. 55-73 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko: "Chaos as a Source of Complexity and Diversity in Evolution" Artificial Life. 1. 163-177 (194)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Tanabe and K.Kaneko: "Behaviors of A Falling Paper" Phys. Rev. Lett.73. 1372-1375 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] F.H.Willeboordse and K.Kaneko: "Bifurcations and Spatial Chaos in an Open Flow Model" Phys. Rev. Lett.73. 533-536 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko: "Information Cascade with Marginal Stability in Network of Chaotic Elements" Physica D. 77. 456-472 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] F.H.Willeboordse and K.Kaneko: "Pattern Dynamics of a Coupled Map Lattice for Open FLow" Physica D. (in press). (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] F.H.Willeboordse and K.Kaneko: "Self-Organized Periodic Lattices of Chaotic Defects" Physical Rev. E.(in press). (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko: "Remarks on the mean field dynamics of network of chaotic elements" Physica D. (in press). (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Yanagita and K.Kaneko: "Rayleigh-Benard Convection : Pattern,Chaos,Spatiotemporal Chaos and Turbulence" Physica D. (in press). (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko and T.Konishi: "Peeling the Onion of Order and Chaos in a High-dimensional Hamiltonian System" Physica D. 71. 146-167 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko: "Relevance of Clustering to Biological Netwirks" Physica D. 55-73 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko: "Chaos as a Source of Complexity and Diversity in Evolution" Artificial Life. 1. 163-177 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Tanabe and K.Kaneko: "Dynamical Behaviors of A Falling Paper" Phys.Rev.Lett.73. 1372-1375 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] F.H.Willeboordse and K.Kaneko: "Bifurcations and Spatial Chaos in as Open Flow Model" Phys.Rev.Lett.73. 533-536 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko: "Information Cascade with Marginal Stability in Network of Chaotic Elements" Physica D. 77. 456-472 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] F.H.Willeboordse and K.Kaneko: "Pattern Dynamics of a Coupled Map Lattice for Open Flow" Physica D. (in press). (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] F.H.Willeboordse and K.Kaneko: "Self-Organized Periodic Lattices of Chaotic Defects" Physical Rev.E.(in press). (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko: "Remarks on the mean field dynamics of network of chaotic elements" Physica D. (in press). (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Yanagita and K.Kaneko: "Rayleign-Benard Convection : Pattern, Chaos, Spatiotemporal Chaos and Turbulence" Physica D. (in press). (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] K.Kaneko and T.Konishi: "Peeling the Onion of Order and Chaos in a High-dimensional Hamiltonian System" Physica D. 71. 146-167 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Kaneko: "Relevance of Clustering to Biological Networks" Physica D. 75. 55-73 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Kaneko: "Chaos as a Source of Complexity and Diversity in Evolution" Artificial Life. 1. 163-177 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] F.H.Willeboordse and K.Kaneko: "Bifurcations and Spatial Chaos in an Open Flow Model" Phys.Rev.Lett.73. 533-536 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Kaneko: "Information Cascade with Marginal Stability in Network of Chaotic Elements" Physica D. 77. 456-472 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Kaneko: "Remarks on the mean field dynamics of network of chaotic elements" Physica D. (in press). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Yanagita and K.Kaneko: "Rayleigh-Benard Convection:Pattern,Chaos,Spatiotemporal Chaos and Turbulence" Physica D. (in press). (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Kaneko and T.Konishi: "Peeling the Onion of Order and Chaos in a High-dimensional Hamiltonian System" Physica D. (in press). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.Kaneko: "Chaos as a Source of Complexity and Diversity in Evolution" Artificial Life 1. (in press). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.Kaneko: "Relevance of Clustering to Biological Networks" Physica D. (in press). (1994)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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