2001 Fiscal Year Annual Research Report

数理生物学における力学系に関する総合的研究

Research Project

Project/Area Number	13304006
Research Institution	Shizuoka University
Principal Investigator	竹内康博静岡大学, 工学部, 教授 (20126783)
Co-Investigator(Kenkyū-buntansha)	原惟行大阪府立大学, 工学研究科, 教授 (20029565) 巌佐庸九州大学, 理学研究科, 教授 (70176535) 三村昌泰広島大学, 理学研究科, 教授 (50068128) 難波利幸大阪女子大学, 理学部, 教授 (30146956) 古用哲夫島根大学, 総合理工学部, 教授 (40039128)
Keywords	数理生物学 / 力学系 / 微分方程式 / 時間遅れ / カオス / パーマネンス
Research Abstract	数理生物学で現れる代表的な力学系の諸性質を総合的に解析することが本研究の目的である。本年の実績は、以下のようにまとめられる。 (1)数理生物学で現れる種々の力学系について、その未解決の問題点とそれを解決するための方法論に関して討議・検討するため静岡大学内部のグループで定期的にセミナー(「力学系セミナー」)を開催した。セミナーは15回行われ、そのレジュメは研究代表者のホームページで公開されている。主要なテーマは人間行動・社会の数理モデル化(中丸):野生生物集団の絶滅と生物多様性維持の数理生物学(佐藤):空間パターン形成の数理生物学(泰中):疫学と免疫学の数理生物学(竹内):非線形システムの力学的安定性に関する数理生物学(宮崎):カオスと数理生物学(ゲスト):数値解析と数理生物学(ゲスト)である。 (2)7月16-19日とハワイ州ヒロで数理生物学国際会議日米シンポジウム2001を研究代表者がオーガナイザーの一人として開催し、数理生物学における力学系に関して討議をした。研究分担者のほとんどもこの会議に参加した。 (3)8月6日-9日と高野山大学で研究集会「関数微分方程式高野山セミナー2001」を開催した。 (4)11月16・17日と岡山大学環境理工学部で研究集会「数理解析の環境問題への応用」を開催した。来年度は上記(1)での成果をもとに、5月下旬に数理生物学における力学系をテーマにワークショップを開催する予定であり、今後3年間で解決すべき課題とその方法に関して討議を行う。本ワークショップには個体群数理生物学と進化ゲームにおける世界的権威者である、ウィーン大学数学科教授のJosef Hofbauerも参加予定である。また、7月には海外共同研究者であるイタリアのウルビノ大学教授が主催する数理生物学ヨーロッパサマーセミナーに参加し、共同研究を進める。

Research Products
(35 results)

All Other

All Publications (35 results)

[Publications] E.Beretta: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Analysis,Theory,Methods and Applications. 47・6. 4107-4115 (2001)
[Publications] R.Kon: "The invadibility of a host in host-parasitoid systems"Differential Equations and Dynamical Systems. 9・1. 63-82 (2001)
[Publications] Bo.Feng: "A stage-structured time-delay model of single-species exposed to environmental hormone"Nonlinear Analysis,Theory,Methods and Applications. 47・6. 4059-4069 (2001)
[Publications] R.Kon: "Permanence of host-parasitoid systems"Nonlinear Analysis,Theory,Methods and Applications. 47・2. 1383-1393 (2001)
[Publications] Y.Takeuchi: "Global stability of Lotka-Volterra prey-predator systems with spatial heterogeneity"Differential Equations and Dynamical Systems. 9・1. 23-36 (2001)
[Publications] E.Beretta: "Nonexistence of periodic solutions in a class of delay-differential equations"Proc.Dyna.Sys.Appl. 3. 69-76 (2001)
[Publications] K.Tainaka: "Spatial pattern formation in a model ecosystem: Exchange between symbiosis and competition"Phys.Lett.A. 282. 373-379 (2001)
[Publications] T.Tao: "Glass Transition on Destructed Lattice"Trans.Materials Research Society Japan. 26. 441-444 (2001)
[Publications] K.Tainaka: "Physics and ecology of rock-paper-scissors game"Lecture Notes in Computer Science. 2063. 394-406 (2001)
[Publications] 中丸麻由子: "DDTの生態リスク評価:生物濃縮がもたらすセグロカモメ集団の絶滅リスクの試算"環境科学会誌. 14・1. 61-72 (2001)
[Publications] M.Nakamaru: "Extinction Risk to Herring Gull populations from DDT Exposure"Environmental Toxicology and Chemistry. 21. 195-202 (2002)
[Publications] M.Rodrigo: "Exact solutions of reaction-diffusion systems and nonlinear wave equations"Japan J.Industrial and Appl.Mathematics. 18. 647-656 (2001)
[Publications] R.Kon: "The effect of evolution on host-parasitoid systems"J.Theoretical Biology. 209・3. 287-302 (2001)
[Publications] T.Naito: "Boundedness and almost periodicity in dynamical systems"Journal of Difference Equations and Applications. 7・4. 507-528 (2001)
[Publications] N.Nakagiri: "Indirect Relation between Species Extinction and Habitat Destruction"Ecological Modelling. 137. 109-118 (2001)
[Publications] T. Sakata: "Genetic Interaction on Lattice Space: Relatedness in Small Populations"Trans.Materials Research Society Japan. 26. 437-440 (2001)
[Publications] N.Nakagiri: "Trade-off between Diffusion and Reaction in Lattice System"Trans.Materials Research Society Japan. 26. 445-448 (2001)
[Publications] N.Nakagiri: "Indirect Effects and Parity Law in Interacting Particle Systems"Trans.Materials Research Society Japan. 26. 449-452 (2001)
[Publications] S.Petrovskii: "Some exact solutions of a generalized Fisher equation related to the problem of biological invasion"Mathematical Biolsciences. 172. 73-94 (2001)
[Publications] Y.Hamaguchi: "Modeling spawning strategy for sex change under social control in haremic angelfishes"Behavioral Ecology. 13. 75-82 (2002)
[Publications] T.Hara: "Dynamics of a delay differential system with periodically oscillatory coefficients"Nonlinear Anal.. 47. 4399-4408 (2001)
[Publications] H.Matsunaga: "Global attractivity for a nonlinear difference equation with variable delay"Comput.Math.Appl.. 41. 543-551 (2001)
[Publications] H.Matsunaga: "Global attractivity for a logistic equation with piecewise constant argument"Nonlinear Differential Equations Appl.. 8. 45-52 (2001)
[Publications] Y, Saito: "A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays"J.Math.Anal.Appl.. 256. 162-174 (2001)
[Publications] D.Hilhorst: "A competition-diffusion system approximation to the classical two-phase Stefan problem"Japan J.Industrial and Appl.Mathematics. 18. 161-180 (2001)
[Publications] S.Kawaguchi: "Hormone-mediated patterns formation in seeding of plants: a competitive growth dynamics model"J.Phys.Soc.Japan. 70. 3155-3160 (2001)
[Publications] D.Hilhorst: "Vanishing latent heat limit in a Stefan-like problem arising in Biology"Nonlinear Analysis. (to appear).
[Publications] K.Osaki: "Exponential attractor for a chemotaxis-growth system of equations"Nonlinear Anal.,Series A. (to appear).
[Publications] M.Funaki: "Travelling front solutions arising in a chemotaxis-growth model"J.Math.Biol.. (to appear).
[Publications] S.Petrovskii: "Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species"Japan Journal of Industrial and Applied Mathematics. 18. 459-481 (2001)
[Publications] Y, Saito: "Harmless delays for permanence and impersistence of Lotka-Volterra discrete predator-prey system"Nonlinear Anal.. (to appear).
[Publications] 難波利幸: "食物網とカオス:雑食は少数自由度系と大自由度系を結ぶ鍵になるか?"物性研究. 77・3. 524-528 (2001)
[Publications] T.A.Burton: "Fixed points and problems in stability theory for ordinary and functional differential equations"Dynamic Systems and Applications. 10. 89-116 (2001)
[Publications] T.A.Burton: "A note on stability by Schauder's theorem"Funkcialaj Ekvacioj. 44. 73-82 (2001)
[Publications] 竹内康博: "進化ゲームと微分方程式"現代数学社. 407 (2001)

2001 Fiscal Year Annual Research Report

数理生物学における力学系に関する総合的研究

Principal Investigator

竹内 康博 静岡大学, 工学部, 教授 (20126783)

Research Products

[Publications] E.Beretta: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Analysis,Theory,Methods and Applications. 47・6. 4107-4115 (2001)

[Publications] R.Kon: "The invadibility of a host in host-parasitoid systems"Differential Equations and Dynamical Systems. 9・1. 63-82 (2001)

[Publications] Bo.Feng: "A stage-structured time-delay model of single-species exposed to environmental hormone"Nonlinear Analysis,Theory,Methods and Applications. 47・6. 4059-4069 (2001)

[Publications] R.Kon: "Permanence of host-parasitoid systems"Nonlinear Analysis,Theory,Methods and Applications. 47・2. 1383-1393 (2001)

[Publications] Y.Takeuchi: "Global stability of Lotka-Volterra prey-predator systems with spatial heterogeneity"Differential Equations and Dynamical Systems. 9・1. 23-36 (2001)

[Publications] E.Beretta: "Nonexistence of periodic solutions in a class of delay-differential equations"Proc.Dyna.Sys.Appl. 3. 69-76 (2001)

[Publications] K.Tainaka: "Spatial pattern formation in a model ecosystem: Exchange between symbiosis and competition"Phys.Lett.A. 282. 373-379 (2001)

[Publications] T.Tao: "Glass Transition on Destructed Lattice"Trans.Materials Research Society Japan. 26. 441-444 (2001)

[Publications] K.Tainaka: "Physics and ecology of rock-paper-scissors game"Lecture Notes in Computer Science. 2063. 394-406 (2001)

[Publications] 中丸麻由子: "DDTの生態リスク評価:生物濃縮がもたらすセグロカモメ集団の絶滅リスクの試算"環境科学会誌. 14・1. 61-72 (2001)

[Publications] M.Nakamaru: "Extinction Risk to Herring Gull populations from DDT Exposure"Environmental Toxicology and Chemistry. 21. 195-202 (2002)

[Publications] M.Rodrigo: "Exact solutions of reaction-diffusion systems and nonlinear wave equations"Japan J.Industrial and Appl.Mathematics. 18. 647-656 (2001)

[Publications] R.Kon: "The effect of evolution on host-parasitoid systems"J.Theoretical Biology. 209・3. 287-302 (2001)

[Publications] T.Naito: "Boundedness and almost periodicity in dynamical systems"Journal of Difference Equations and Applications. 7・4. 507-528 (2001)

[Publications] N.Nakagiri: "Indirect Relation between Species Extinction and Habitat Destruction"Ecological Modelling. 137. 109-118 (2001)

[Publications] T. Sakata: "Genetic Interaction on Lattice Space: Relatedness in Small Populations"Trans.Materials Research Society Japan. 26. 437-440 (2001)

[Publications] N.Nakagiri: "Trade-off between Diffusion and Reaction in Lattice System"Trans.Materials Research Society Japan. 26. 445-448 (2001)

[Publications] N.Nakagiri: "Indirect Effects and Parity Law in Interacting Particle Systems"Trans.Materials Research Society Japan. 26. 449-452 (2001)

[Publications] S.Petrovskii: "Some exact solutions of a generalized Fisher equation related to the problem of biological invasion"Mathematical Biolsciences. 172. 73-94 (2001)

[Publications] Y.Hamaguchi: "Modeling spawning strategy for sex change under social control in haremic angelfishes"Behavioral Ecology. 13. 75-82 (2002)

[Publications] T.Hara: "Dynamics of a delay differential system with periodically oscillatory coefficients"Nonlinear Anal.. 47. 4399-4408 (2001)

[Publications] H.Matsunaga: "Global attractivity for a nonlinear difference equation with variable delay"Comput.Math.Appl.. 41. 543-551 (2001)

[Publications] H.Matsunaga: "Global attractivity for a logistic equation with piecewise constant argument"Nonlinear Differential Equations Appl.. 8. 45-52 (2001)

[Publications] Y, Saito: "A necessary and sufficient condition for permanence of a Lotka-Volterra discrete system with delays"J.Math.Anal.Appl.. 256. 162-174 (2001)

[Publications] D.Hilhorst: "A competition-diffusion system approximation to the classical two-phase Stefan problem"Japan J.Industrial and Appl.Mathematics. 18. 161-180 (2001)

[Publications] S.Kawaguchi: "Hormone-mediated patterns formation in seeding of plants: a competitive growth dynamics model"J.Phys.Soc.Japan. 70. 3155-3160 (2001)

[Publications] D.Hilhorst: "Vanishing latent heat limit in a Stefan-like problem arising in Biology"Nonlinear Analysis. (to appear).

[Publications] K.Osaki: "Exponential attractor for a chemotaxis-growth system of equations"Nonlinear Anal.,Series A. (to appear).

[Publications] M.Funaki: "Travelling front solutions arising in a chemotaxis-growth model"J.Math.Biol.. (to appear).

[Publications] S.Petrovskii: "Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species"Japan Journal of Industrial and Applied Mathematics. 18. 459-481 (2001)

[Publications] Y, Saito: "Harmless delays for permanence and impersistence of Lotka-Volterra discrete predator-prey system"Nonlinear Anal.. (to appear).

[Publications] 難波利幸: "食物網とカオス:雑食は少数自由度系と大自由度系を結ぶ鍵になるか?"物性研究. 77・3. 524-528 (2001)

[Publications] T.A.Burton: "Fixed points and problems in stability theory for ordinary and functional differential equations"Dynamic Systems and Applications. 10. 89-116 (2001)

[Publications] T.A.Burton: "A note on stability by Schauder's theorem"Funkcialaj Ekvacioj. 44. 73-82 (2001)

[Publications] 竹内康博: "進化ゲームと微分方程式"現代数学社. 407 (2001)

竹内康博静岡大学, 工学部, 教授 (20126783)