A study on difference equations in mathematical biology with Lotka-Volterra equations

• Project/Area Number: 25800095
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: University of Miyazaki
• Principal Investigator: Kon Ryusuke 宮崎大学, 工学教育研究部, 准教授 (10345811)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); 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); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: Lotka-Volterra方程式 / Leslie行列モデル / 1回繁殖型 / 連続化 / 離散化 / 非線形差分方程式 / 非線形常微分方程式 / 分岐 / Leslie行列 / 生物数学 / 漸近安定性 / 周期解 / Leslieモデル / 一回繁殖型 / 差分方程式 / Liapunovの方法 / 大域漸近安定性

Outline of Final Research Achievements

Biological phenomena are often described by difference equations. Some of the difference equations are formally approximated by Lotka-Volterra equations. This study gives a mathematical base to this approximation and shows that some bifurcation problems of difference equations can be reduced to stability problems of Lotka-Volterra equations. The analytical tools for difference equations are poorer than those for differential equations. Our study gives a new method for understanding the behavior of difference equations.

Research Products

• [Journal Article] 周期ゼミの素数年周期と周期的な捕食圧16-23. (2015)
  • Author(s): 今 隆助
  • Journal Title: 応用数理 Volume: 25(4) Pages: 16-23
  • Peer Reviewed / Open Access
• [Journal Article] Dynamics of competitive systems with a single common limiting factor (2015)
  • Author(s): Ryusuke Kon
  • Journal Title: Mathematical Biosciences and Engineering Volume: 12 Pages: 71-81
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 一回繁殖型の非線形Leslie モデルの連続化と分岐解析 (2015)
  • Author(s): 今隆助
  • Journal Title: 研究集会報告(26AO-S2)「非線形波動研究の現状ー課題と展望を探るー」 Volume: 26AO-S2 Pages: 94-100
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] 回繁殖型非線形Leslie行列モデルの大域漸近安定性, 数理解析研究所講究録 (2014)
  • Author(s): 今隆助
  • Journal Title: 数理解析研究所講究録 Volume: 1917 Pages: 153-158
  • Open Access / Acknowledgement Compliant
• [Presentation] 宿主・捕食寄生者モデルの超離散化と非有界性 (2015)
  • Author(s): 今 隆助
  • Organizer: RIMS研究集会「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420号室
  • Year and Date: 2015-11-24
• [Presentation] 一回繁殖型Leslie行列モデルにおける周期解の分岐 (2015)
  • Author(s): 今 隆助
  • Organizer: 日本数学会2015年度秋季総合分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-13
• [Presentation] Dynamics of nearly-semelparous Leslie matrix models (2015)
  • Author(s): Ryusuke Kon
  • Organizer: 2015 Joint Meeting of JSMB and CJK Colloquium on Mathematical Biology
  • Place of Presentation: 同志社大学
  • Year and Date: 2015-08-26
  • Int'l Joint Research
• [Presentation] Bifurcating of cycles in nonliear semelparous Leslie matrix models (2015)
  • Author(s): Ryusuke Kon
  • Organizer: 2015 Joint Meeting of JSMB and CJK Colloquium on Mathematical Biology
  • Place of Presentation: 同志社大学
  • Year and Date: 2015-08-26
  • Int'l Joint Research / Invited
• [Presentation] 一回繁殖型の非線形Leslie モデルの連続化と分岐解析 (2014)
  • Author(s): 今 隆助
  • Organizer: 平成２６年度九大応力研共同利用研究集会「非線形波動研究の現状―課題と展望を探る―」
  • Place of Presentation: 九州大学応用力学研究所
  • Year and Date: 2014-10-31 – 2014-11-01
  • Invited
• [Presentation] 一回繁殖型Leslieモデルの同期周期軌道の安定性 (2014)
  • Author(s): 今 隆助
  • Organizer: RIMS研究集会「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420号室
  • Year and Date: 2014-09-16
• [Presentation] Dynamics of competitive systems with a single common limiting factor (2014)
  • Author(s): Ryusuke Kon
  • Organizer: The Joint Annual Meeting of the Japanese Society for Mathematical Biology and the Society for Mathematical Biology (JSMB/SMB 2014 Osaka)
  • Place of Presentation: Osaka, Japan
  • Year and Date: 2014-07-28 – 2014-08-01
• [Presentation] Bifurcation and global stability of nonlinear semelparous Leslie matrix models (2013)
  • Author(s): Ryusuke Kon
  • Organizer: The 4th International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems
  • Place of Presentation: Texas Tech University, Lubbock TX, USA
  • Invited
• [Presentation] semelparous なLeslie 行列モデルの分岐と大域安定性 (2013)
  • Author(s): 今 隆助
  • Organizer: RIMS研究集会「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420号室
  • Invited
• [Presentation] Leslie行列モデルの分岐とLotka-Volterra方程式 (2013)
  • Author(s): 今 隆助
  • Organizer: 第129回 日本数学会九州支部例会
  • Place of Presentation: 宮崎大学工学部Ｄ棟2階プレゼンテーション室
  • Invited
• [Remarks] 今隆助のwebページ
  • URL: http://www.cc.miyazaki-u.ac.jp/konr/