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2007 Fiscal Year Final Research Report Summary

Mathematical Structure for Forest Bynamics with Interaction between Trees and Soils

Research Project

Project/Area Number 16340046
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionOsaka University

Principal Investigator

YAGI Atsushi  Osaka University, Graduate School of Engineering, Professor (70116119)

Co-Investigator(Kenkyū-buntansha) KASAI Hideaki  Osaka University, Graduate School of Engineering, Professor (00177354)
MATSUMURA Akitaka  Osaka University, Graduate School of Information Science and Technobgy, Professor (60115938)
ODANAKA Shinji  Osaka University, CybermediaCenter, Professor (20324858)
TSUJIKAWA Tohru  Miyazaki University, Faculty of Engineering, Professor (10258288)
TABATA Minoru  Osaka Prefecture University, Graduate School of Engineering, Professor (70207215)
Project Period (FY) 2004 – 2007
KeywordsForest kinematic model / Nonlinear differential equations / Dynamical system / Self-orvanization / Numerical simulation / Forest boundary
Research Abstract

We are concerned with the dynamics of forest system. Considering the system as a hybrid system of trees and soils with some interactions, we introduced a mathematical model which describes the kinetics of system. The model is expressed by a system of nonlinear partial differential equations. In this research program we have studied analytically and numerically the model mainly in a case where the soil level is constant and stable. In such a case we constructed a dynamical system determined from the model equations, constructed a Iyapunov function for the dynamical system, showed that every trajectory converges asymptotically to a stationary solution and clarified that the structure of equilibria, i.e., stationary solutions of model equations, changes drastically depending on the various parameters in the equations which represent the state of the forest. Furthermore we have found out that this model gives us a clear boundary which may seem to correspond to the forest boundary which the forest possesses inherently: This means that observing the best boundary we can inversely identify all the parameters in the model to know the mathematical structure of the forest system. This suggests, furthermore, that it is possible in the future to know from observations of the bust boundary the degree of health or the power of restitution from destruction for the forest itself. As for the case where the soil level is non constant and unstable, we have only performed numerical simulations. We found out some interesting quasi-periodic trajectories. But the mathematical analysis remains to be studied in the future.

  • Research Products

    (10 results)

All 2006 2005

All Journal Article (7 results) (of which Peer Reviewed: 3 results) Presentation (2 results) Book (1 results)

  • [Journal Article] Dynamical system for forest kinematic model2006

    • Author(s)
      L. H. Chuan(他)
    • Journal Title

      Advances Mathematical Sciences Applications 16

      Pages: 393-409

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions for forest kinematic model2006

    • Author(s)
      L. H. Chuan(他)
    • Journal Title

      Funkcialaj Ekvacioj 49

      Pages: 427-449

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Dynamical system for forest kinematic model2006

    • Author(s)
      L. H., Chuan, et. al.
    • Journal Title

      Advances Mathematical Sciences Application 16-2

      Pages: 393-409

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Asymptotic behavior of solutions for forest kinematic model2006

    • Author(s)
      L. H., Chuan, et. al.
    • Journal Title

      Funkcialaj Ekvacioj 49-3

      Pages: 427-449

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] (division of lot), Annual Report of FY 2005, Core University Program JSPS and Vast2006

    • Author(s)
      M., Ike H., Viet, A., Yagi, et. al.
    • Journal Title

      Ike Lab. Graduate School of Engineering, Osaka University

      Pages: 285.288

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Quasilinear abstract evolution equations and exponential attractors2005

    • Author(s)
      M. Aida(他)
    • Journal Title

      Osaka Journal Mathematics 42

      Pages: 101-132

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Quasilinear abstract evolution equations and exponential attractors2005

    • Author(s)
      M., Aida, et. al.
    • Journal Title

      Osaka Journal Mathematics 42

      Pages: 1

    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] ω-limit sets of dynamical system for forest kinematic model2006

    • Author(s)
      L. H. Chuan(他)
    • Organizer
      日本数学会春季年会函数解析学分科会
    • Place of Presentation
      中央大学
    • Year and Date
      2006-03-26
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] w-limit sets of dynamical system for forest kinematic model2006

    • Author(s)
      L. H., Chuan, et. al.
    • Organizer
      Annual Meeting Mathematical Society Japan
    • Place of Presentation
      Chug University
    • Year and Date
      2006-03-26
    • Description
      「研究成果報告書概要(欧文)」より
  • [Book] Annual Report of FY2005, Core University Program JSPS and VAST2006

    • Author(s)
      M. Ike and H. Viet(編集), A. Yagi, T. Miyagi and P. N. Hong(分担)
    • Total Pages
      285-288
    • Publisher
      大阪大学大学院工学研究科環境・エネルギー工学専攻 池 研究室
    • Description
      「研究成果報告書概要(和文)」より

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Published: 2010-02-04  

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