Theory on Stabilizing Differential Equations in Mathematical Ecology

• Project/Area Number: 26800080
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Shimane University
• Principal Investigator: Saito Yasuhisa 島根大学, 総合理工学研究科, 准教授 (30402241)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: パーマネンス / リミットサイクル / 大域的漸近安定性 / 生物の移動 / 漸近安定化

Outline of Final Research Achievements

I had tried to figure up how species dispersal and environmental fluctuations stabilize mathematical-ecologically fundamental systems of Lotka-Volterra equations and Rosezweig-MacArthur equations where so called "ecological instability" can be observed. Some results of them have been derived and I am now writing papers on them.

Research Products

• [Presentation] 生物的防除における系の大域漸近安定性とリミットサイクルについて (2017)
  • Author(s): 齋藤保久
  • Organizer: 研究集会「生命動態とその数理」
  • Place of Presentation: 松江エクセルホテル東急
  • Year and Date: 2017-02-19
  • Invited
• [Presentation] Permanence, global stability, and limit cycle on some predator-prey systems (2016)
  • Author(s): Yasuhisa Saito
  • Organizer: PNU MATH FORUM 2016
  • Place of Presentation: Pusan Naitonal University, Korea
  • Year and Date: 2016-12-01
  • Int'l Joint Research / Invited
• [Presentation] 間接効果を考慮したpredator-prey系の大域的漸近安定性とリミットサイクルについて (2016)
  • Author(s): 齋藤保久
  • Organizer: ＲＩＭＳ研究集会 第13回「生物数学の理論とその応用」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2016-11-14
• [Presentation] リエナール方程式のある応用について (2016)
  • Author(s): 齋藤保久
  • Organizer: 常微分方程式の定性的理論ワークショップ
  • Place of Presentation: 島根大学松江キャンパス
  • Year and Date: 2016-09-22
  • Invited
• [Presentation] Lyapunov functions and some predator-prey differential equations (2016)
  • Author(s): Yasuhisa Saito
  • Organizer: JSMB2016
  • Place of Presentation: 九州大学伊都キャンパス
  • Year and Date: 2016-09-07
  • Invited
• [Presentation] 宿主被食による寄生者拡散を考慮した宿主寄生者微分方程式について (2015)
  • Author(s): 小國仁嗣、齋藤保久
  • Organizer: 第二回 ODE 若手セミナー
  • Place of Presentation: 岡山理科大学
  • Year and Date: 2015-12-03
• [Presentation] Coexistence promoted by species migration in predator-prey models (2014)
  • Author(s): Yasuhisa SAITO
  • Organizer: The Joint Annual Meeting of JSMB/SMB 2014 Osaka
  • Place of Presentation: Osaka International Convention Center
  • Year and Date: 2014-07-28 – 2014-08-01