| 具有不依赖于时间的不变量的三维常微分方程组的Hamilton结构 |
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| 引用本文： | 郭仲衡,陈玉明.具有不依赖于时间的不变量的三维常微分方程组的Hamilton结构[J].应用数学和力学,1995,16(4):283-288. |
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| 作者姓名： | 郭仲衡 陈玉明 |
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| 作者单位： | 1.北京大学数学系 100871; |
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| 摘 要： | 本文证明了具有不依赖于时间的不变量的三维常微分方程组所描述的动力系统相对于一广义Poisson括号可以改写为Hamilton系统,并且这些不变量就是Hamilton量。作为例子,我们讨论了Kermack-Mckendrick传染病模型,所得结果推广了Y.Nutku的结果。
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| 关 键 词： | Poisson括号 Hamilton结构 bi-Hamilton结构 不变量 Kermack-Mckendrick传染病模型 |
| 收稿时间： | 1994-04-01 |
The Hamiltonian Structures of 3D ODE with Time-Independent Invariants |
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| Guo Zhong-heng.The Hamiltonian Structures of 3D ODE with Time-Independent Invariants[J].Applied Mathematics and Mechanics,1995,16(4):283-288. |
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| Authors: | Guo Zhong-heng |
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| Institution: | 1.Department of Mathematics, Peking University, Beijing, 100871;2.Department of Applied Mathematics, Hu'nan University, Changsha, 410012 |
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| Abstract: | We have proved that any 3-dimensional dynamical system of ordinary differ-ential equations(in short,3D ODE) with time-independent invariants can be rewritten as Hamiltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants.As an example,we discuss the Ker-mack-Mckendricd model for epidemics in detail.The results we obtained are generalization of those obtained by Y. Nutku. |
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| Keywords: | Poisson bracket Hamiltonian structure bi-Hamiltonian structure Invariant the Kermack-Mckendrick model for epidemics |
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