关键词: Lotka-Volterra系统, 广义Poisson括号, 广义Hamilton结构, 双Hamilton结构

Abstract: We considered two LotkaVolterra system with three degrees of freedom. Firstly, we introduced the generalized Poissonbracket and generalized Hamiltonian structures in threedimensional systems. Secondly,  we observed the first integral of the system by constructing local homeomorphism transformation and established the algebraic equation. The Hamiltonian function of the system was obtained by solving the algebraic equation. Finally, we gave  the sufficient conditions for the existence of BiHamiltonian structure of LotkaVolterra system.

Key words: LotkaVolterra system, generalized Poissonbracket, generalized Hamiltonian structure, BiHamiltonian structure