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。
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.
出处
《应用数学和力学》
CSCD
北大核心
1995年第4期283-288,共6页
Applied Mathematics and Mechanics
关键词
K-M传染病模型
常微分方程组
哈密顿结构
Poisson bracket,Hamiltonian structure,bi-Hamiltonian structure,Invariant,the Kermack-Mckendrick model for epidemics