A study on difference equations in mathematical biology with Lotka-Volterra equations
| Project/Area Number |
25800095
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | University of Miyazaki |
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Principal Investigator |
Kon Ryusuke 宮崎大学, 工学教育研究部, 准教授 (10345811)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥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)
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| 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 |
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| 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.
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Report
(4 results)
Research Products
(15 results)
