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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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。
- Poisson括号 /
- Hamilton结构 /
- bi-Hamilton结构 /
- 不变量 /
- Kermack-Mckendrick传染病模型
Abstract: We have proved that any 3-dimensional dynamical system of ordinary differential equations(in short, 3D ODE)With time-independent invariants can be rewritten as Haniltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants. As an example,we discuss the Kermack-Mckendrick modelfor epidemics in detail. The results we obtained are generalization of those obtained by Y. Nutku.
- Poisson bracket /
- Hamiltonian structure /
- bi-Hamiltonianstructure /
- invariant /
- the Kermack-Mckendrick model for epidemics

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