三维Lotka-Volterra系统的双Hamilton结构

Bi-Hamiltonian Structure of Three-Dimensional Lotka-Volterra System

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。

We considered two Lotka-Volterra system with three degrees of fr eedom. Firstly,we introduced the generalized Poisson-bracket and generalized Ha miltonian structures in three-dimensional systems. Secondly, we observed the firs t integral of the system by constructing local homeomorphism transformation and established the algebraic equation. The Hamiltonian function of the system was obtai ned by solving the algebraic equation. Finally,we gave the sufficient conditions for the ex istence of Bi-Hamiltonian structure of Lotka-Volterra system.