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Chaotic Phenomena and Their Engineering Relevance

Research Project

Project/Area Number 05044091
Research Category

Grant-in-Aid for international Scientific Research

Allocation TypeSingle-year Grants
SectionJoint Research
Research InstitutionKyoto University

Principal Investigator

UEDA Yoshisuke  Faculty of Eng., Kyoto University, Professor, 工学部, 教授 (00025959)

上田 皖亮  京都大学, 工学部, 教授

Co-Investigator(Kenkyū-buntansha) MCROBIE F.Allan  University College London (Royal Society University Research Fellow), ロイヤルソサエティリ
STEWART H.Bruce  Brookhaven National Laboratory (Mathematician), 数学者
Project Period (FY) 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1993: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsNolinear dynamical systems / Simulation experiments / Bifurcation / Indeterminate outcome / Minorsky equation / Basin boundary / Straddle orbit method / 位相同期系
Research Abstract

The objective of research is to understand the behavior of nonlinear dynamical systems using theory and extensive numerical simulation. Prototype models including second-order oscillators have been selected to include some previously neglected but essential properties of real physical and engineering systems. Basic insight is gained by avoided unnecessary camplications.
A comprehensive review and classification of hifurcations involving one parameter was completed. Safe, explosive and dangerous types were distinguished, and related to phenomena of fundamental concern in applications : continuity or discontinuity of responses, hysteresis, intermittency and indeterminate outcomes. Study of escape from potential wells was extended to a wide range of volues of the damping coefficient. The close connection between optimal escape and resonance was confirmed ; subtle but important changes in bifurcation patterns were discovered, and their significance for experimental studies was clarified.
We have considered the nonlinear dynamical system with time delay described by the Minorsky equation (see Minorsky, J.Appl.Phys, Vol.19, 1948), which he introduced during his studies of active ship stabilization. Differential equations with a time delay, sometimes called differential-difference equations, have an infinite dimensional phase space. The global features of the basin boundaries are not easily grasped, but they have great practical importance.
In earlier work, we made some progress by making 'carpet bombing' experiments from a grid of starts in one cross-section of the phase space : but now we have focused attention on the unstable basic sets governing the basin boundaries, which we have located numerically using the straddle orbit technique. This approach gives much more insight into basin structure than carpet bombing ; for example, a stability index involving distance from attracter to unstable basic set may be computed. This will be pursued in future research.

Report

(1 results)
  • 1993 Final Research Report Summary
  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] 喜多敏博,野尻引輔,上田〓亮: "電力系統に生じるカオス的動揺現象" 電気学会電力技術研究会資料. PE93-2. 7-16 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Mitsui,Y.Ueda and J.M.T.Thompson: "Basic Sets Separating Two Coexisting Oscillations in a Delayed System" Proc.1993 Int.Symp.Nonlinear Theory and Its Applications(NOLTA'93). Vol.3. 811-814 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] H.Ito,K.Harada and Y.Ueda: "Self-Generated Chaos in a Spatially Extended System with Two Types of Instabilities" Proc.1993 Int.Symp.Nonlinear Theory and Its Applications(NOLTA'93). Vol.3. 1015-1018 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Mitsui,Y.Ueda and J.M.T.Thompson: "Straddle-Orbit Location of a Chaotic Saddle in a High-Dimensional Realization.of R∞" Proc.Royal Society London(A). (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] J.M.T.Thompson,H.B.Stewart and Y.Ueda: "Safe,Explosive,and Dangerous Bifurcations in Dissipative Dynamical Systems" Physical Review E. Vol.49 No.1. (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Y.Ueda,H.Ohta and H.B.Stewart: "Bifurcations in a System Described by a Nonlinear Differential Equation with Delay" Chaos,American Institute of Physics. Vol.4 No.1. (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] H.B.Stewart,J.M.T.Thompson,Y.Ueda and A.N.Lansbury: "Optimal Escape from Potential Wells-Patterns of Regular and Chaotic Bifurcation" (未定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Kita, K.Nojiri and Y.Ueda: "Chaotic swing phenomena in an electric power system" Technical Report of Inst.Elec.Engrs. PE93-2. 811-814 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Mitsui, Y.Ueda and J.M.T.Thompson: "Basic sets separating two coexisting oscillations in a delayed system" Proc. 1993 Inst. Symp. Nonlinear Theory and Its Applications. 3. 811-814 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] H.Ito, K.Harada and Y.Ueda: "Self-generated chaos in a spatially extended system with two types of instabilities" Proc. 1993 Int. Symp. Nonlinear Theory and Its Applications. 3. 1015-1018 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Mitsui, Y.Ueda and J.M.Thompson: "Straddle-orbit location of a chaotic saddle in a high-dimensional realization of R*" Proc. Royal Society London(A). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] J.M.T.Thompson, H.B.Stewart and Y.Ueda: "Safe, explosive, and dangerous bifurcations in dissipative dynamical systems" Physical Review E. 49. (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Y.Ueda, H.Ohta and H.B.Stewart: "Bifurcation in a system described by a nonlinear differential equation with delay" Chaos, American Institute of Physics. 4. (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] H.B.Stewart, J.M.T.Thompson, Y.Ueda and A.N.Lansbury: in preparation. Optimal escape from potential well-Patterns of regular and chaotic bifurcation,

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary

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

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