| 三维Lotka-Volterra系统的双Hamilton结构 |
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| 引用本文： | 许明星,周冉.三维Lotka-Volterra系统的双Hamilton结构[J].吉林大学学报(理学版),2019,57(4):773-778. |
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| 作者姓名： | 许明星 周冉 |
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| 作者单位： | 吉林大学数学学院,长春,130012;吉林大学数学学院,长春,130012 |
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| 基金项目： | 吉林省科技发展计划项目 |
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| 摘 要： | 考虑两个具有3个自由度的Lotka Volterra系统, 首先介绍三维系统中广义Poisson括号和广义Hamilton结构； 然后通过构造局部同胚变换, 观察得到系统的首次积分, 建立代数方程, 求解得到系统的Hamilton函数； 最后给出Lotka-Volterra系统存在双Hamilton结构的充分性条件.
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| 关 键 词： | Lotka-Volterra系统 广义Poisson括号 广义Hamilton结构 双Hamilton结构 |
| 收稿时间： | 2019-03-22 |
Bi-Hamiltonian Structure of Three-Dimensional Lotka-Volterra System |
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| XU Mingxing,ZHOU Ran.Bi-Hamiltonian Structure of Three-Dimensional Lotka-Volterra System[J].Journal of Jilin University: Sci Ed,2019,57(4):773-778. |
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| Authors: | XU Mingxing ZHOU Ran |
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| Institution: | College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | We considered two Lotka Volterra system with three degrees of freedom. Firstly, we introduced the generalized Poisson bracket and generalized Hamiltonian structures in three dimensional systems. Secondly, we observed the first integral of the system by constructing local homeomorphism transformation and established the algebraic equation. The Hamiltonian function of the system was obtained by solving the algebraic equation. Finally, we gave the sufficient conditions for the existence of Bi Hamiltonian structure of Lotka Volterra system. |
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| Keywords: | Lotka Volterra system generalized Poisson bracket generalized Hamiltonian structure Bi Hamiltonian structure
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