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Persistence analysis of mathematical ecological models

Research Project

Project/Area Number 01540177
Research Category

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

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionShizuoka University

Principal Investigator

TAKEUCHI Yasuhiro  Shizuoka Univ. Dept. of Eng. Associate Prof., 工学部, 助教授 (20126783)

Project Period (FY) 1989 – 1991
Project Status Completed (Fiscal Year 1991)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1991: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1990: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1989: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordsmathematical ecology / ecological models / persistence / ordinary differential equations / stability / 微分方程式
Research Abstract

The purpose of this research project is to find out tlie condition for a mathematical ecological model to be persistent. Main neiv results obtained, are as follows :
1. We consider a system composed of two patches connected by diffusion and each patch has two competitors. Conditions for persistence of the system are given. (paper 1).
2. For a system composed of two competitors, one can diffuse between two patches and the other is confined to one of the patches, it is proved that the system can be made persistent under appropriate diffusion conditions, even if the competitive patch is not persistent without diffusion (paper 2).
3. We consider a model composed of two patches. One has three competing species forming a heteroclinic cycle within the patch. The other is a refuge for one of the three species. It is proved that the model can be made persistent even if the underlying cycle is an attractor in the competitive patch (paper 3).
4. We consider a model composed of three refuges and one competitive patch with a heteroclinic cycle. It is shown that Hopf bifurcation is possible when we change the value of diffusion constant and periodic orbits may exist in a specific case (paper 6).

Report

(4 results)
  • 1991 Annual Research Report   Final Research Report Summary
  • 1990 Annual Research Report
  • 1989 Annual Research Report
  • Research Products

    (50 results)

All Other

All Publications (50 results)

  • [Publications] Y.Takeuchi: "Diffusion-mediated persistence in two species competition Lotka-Volterra model" Mathematical Biosciences. 95. 65-83 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Takeuchi: "Conflict between the need to forage and the need to avoid competition:Persistence of two-species model." Mathematical Biosciences. 99. 181-194 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Takeuchi: "Diffusion-mediated persistence in three-species competition models with heteroclinic cycles." Mathematical Biosciences. 106. 111-128 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] H.Matsuda: "Alternative models for species replacement of pelagic fishes." Researches on Population Ecology. 33. 41-56 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] 松田 裕之: "浮魚類魚種交替の三すくみ説における環境変動の効果の理論的検討"

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Takeuchi: "Persistence and periodic orbits of a three-competitor model with refuges." Mathematical Biosciences.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Z.Lu: "Permanence and global stability for cooperative Lotka-Volterra diffusion systems." Non 1 inear Analysis TMA.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Z.Lu: "Global dynamical behavior for Lotka-Volterra systems with a reducible matrix."

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Kuang: "Predator-prey dynamics in models of prey dispersal in two patch environment."

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Z.Lu: "Global asymptotic behavior in single-species discrete diffusion systems."

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Takeuchi: "Refuge-mediated global coexistence of multiple competitors on a single resource."

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Takeuchi: "Global stability of competitive systems with refuges."

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Takeuchi: "Permanence and global stability for competition Lotka-Volterra diffusion systems."

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Z.Lu: "Global stability for a Lotka-Volterra severe competitive system over two patches."

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Takeuchi: "Diffusion-mediated persistence in two species competition Lotka-Volterra model." Math. Biosci.95, No. 1. 65-83 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Takeuchi: "Conflict between the need to forage and the need to avoid competition : Persistence of two-species model." Math. Biosci.99, No. 2. 181-194 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Takeuchi: "Diffusion-mediated persistence in three-species competition models with heteroclinic cycles." Math. Biosci.106, No. 1. 111-128 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] H. Matsuda: "Alternative models for species replacement of pelagic fishes" Res. Popul. Ecol.33, No. 1. 41-56 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] H. Matsuda: "Model analysis of the effect of environmental fluctuation on the species replacement pattern of pelagic fishes in cyclic advantage hypothesis."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Takeuchi: "Persistence and periodic orbits of a three-competitor model with refuges."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Z. Lu: "Permanence and global stability for cooperative Lotka-Volterra diffusion systems."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Z. Lu: "Global dynamical behavior for Lotka-Volterra systems with a reducible matrix."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Kuang: "Predator-prey dynamics in models of prey dispersal in two patch environment."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Z. Lu: "Global asymptotic behavior in single-species discrete diffusion systems."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Takeuchi: "Refuge-mediated global coexistence of multiple competitors on a single resource."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Takeuchi: "Global stability of competitive systems with refuges."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y. Takeuchi: "Permanence and global stability for competition Lotka-Volterra diffusion systems."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Z. Lu: "Global stability for a Lotka-Volterra severe competitive system over two patches."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1991 Final Research Report Summary
  • [Publications] Y.Takeuchi: "Diffusionーmediated persistence in two species competition LotkaーVolterra model" Mathematical Biosciences. 95. 65-83 (1989)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Takeuchi: "Conflict between the need to forage and the need to avoid competition:Persistence of twoーspecies model." Mathematical Biosciences. 99. 181-194 (1990)

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Takeuchi: "Diffusionーmediated persistence in threeーspecies competition models with heteroclinic cycles." Mathematical Biosciences. 106. 111-128 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] H.Matsuda: "Alternative models for species replacement of pelagic fishes." Researches on Population Ecology. 33. 41-56 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] 松田 裕之: "浮魚類魚種交替の三すくみ説における環境変動の効果の理論的検討"

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Takeuchi: "Persistence and periodic orbits of a threeーcompetitor model with refuges." Mathematical Biosciences.

    • Related Report
      1991 Annual Research Report
  • [Publications] Z.Lu: "Permanence and global stability for cooperative LotkaーVolterra diffusion systems." Non 1 inear Analysis TMA.

    • Related Report
      1991 Annual Research Report
  • [Publications] Z.Lu: "Global dynamical behavior for LotkaーVolterra systems with a reducible matrix."

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Kuang: "Predatorーprey dynamics in models of prey dispersal in two patch environment."

    • Related Report
      1991 Annual Research Report
  • [Publications] Z.Lu: "Global asymptotic behavior in singleーspecies discrete diffusion systems."

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Takeuchi: "Refugeーmediated global coexistence of multiple competitors on a single resource."

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Takeuchi: "Global stability of competitive systems with refuges."

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Takeuchi: "Permanence and global stability for competition LotkaーVolterra diffusion systems."

    • Related Report
      1991 Annual Research Report
  • [Publications] Z.Lu: "Global stability for a LotkaーVolterra severe competitive system over two patches."

    • Related Report
      1991 Annual Research Report
  • [Publications] Y.Takeuchi: "Diffusionーmediated persistence in two species competition LotkaーVolterra model" Mathematical Biosciences. 95. 65-83 (1989)

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Takeuchi: "Conflict between the need to forage and the need to avoid competition:Persistence of twoーspecies model" Mathematical Biosciences. 99. 181-194 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Takeuchi: "Diffusionーmediated persistence in threeーspecies competition model with heteroclinic cycles" Mathematical Biosciences.

    • Related Report
      1990 Annual Research Report
  • [Publications] H.Matsuda: "Alternative models for species replacement of pelagic fishes" Research Population Ecology.

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Takeuchi: "Persistence and periodic orbits of threeーcompetitor model with refuges" preprint.

    • Related Report
      1990 Annual Research Report
  • [Publications] 松田 裕之: "浮魚類魚種交替の三すくみ説における環境変動の効果の理論的検討" preprint.

    • Related Report
      1990 Annual Research Report
  • [Publications] Y.Takeuchi: "Diffusion-mediated persistence in two species competition Lotka-Volterra model" Mathematical Biosciences. 95. 65-83 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Y.Takeuchi: "Confict between the need to forage and the need to avoid compition:persistence of two species model." Mathematical Biosciences. (1990)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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