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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.
Guo Zhong-heng, Chen Yu-ming. The Hamiltonian Structures of 3D ODE with Time-Independent Invariants[J]. Applied Mathematics and Mechanics, 1995, 16(4): 283-288.
 Citation: Guo Zhong-heng, Chen Yu-ming. The Hamiltonian Structures of 3D ODE with Time-Independent Invariants[J]. Applied Mathematics and Mechanics, 1995, 16(4): 283-288.

The Hamiltonian Structures of 3D ODE with Time-Independent Invariants

• 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。
•  [1] Nutku, Y., Bi-Hamiltonian structure of the Kermack-Mckendrick model for epidemics, J. Phys. A: Math. Gen., 23(1990), L1145-L1146. [2] Krishnaprasad, P. S. and J. E. Marsden, Hamiltonian structures and stability for rigid bodies with flexible attachments,Arch. Rational Mech. Anal., 98(1987), 71-93. [3] Andrey, L., The rate of entropy change in non-Hamiltonian systems, Phys. Lett. A., 111(1985), 45-46. [4] Gonzalez-Gascon, F., Note on a paper of Andrey concerning non-Hamiltonian systems, Phys. Lett. A., 114(1986), 61-62. [5] Nutku, Y., Hamiltonian structure of the Lotka-Volterra equations, Phvs. Lett. A., 145(1990), 27-28. [6] Olver, P. J., Applications of Lie Groups to Differential Eguations, Springer-Verlag, New York Inc. (1986). [7] John, F., Partial Differential Eguations, 4th ed., Springer-Verlag, New York(1982).

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出版历程
• 收稿日期:  1994-04-01
• 刊出日期:  1995-04-15

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