Polynomial First Integral Of Reversible Lotka-Volterra Model In Belousov-Zhabotinsky Reaction

In this paper, we consider the polynomial first integral for reversible Lotka-Volterra model which describes the oscillatory chemical dynamics in a closed isothermal reaction.This article is divided into three chapters. The first chapter mainly introduces the back-ground of Belousov-Zhabotinsky chemical reactions and the related results, and gives the reversible Lotka-Volterra reaction which in the closed system and at the same time gives the mathematical model of reversible Lotka-Volterra reaction the k1, k2, k3 are positive reaction rates, k-1,k-2, k-3 are reverse reaction rates, x1,x2,x3,x4 represent the rates of the change of X, Y, A, B.The second chapter is preliminary knowledge. First we give the definitions of the first integral and the integrability for differential equation, then introduce some necessary con-ditions about the existence and nonexistence of first integral, at the last introduce the semi-quasihomogeneous system and some related results.The third chapter studies the first integral of reversible Lotka-Volterra model, we could regard the equation as a semiquasihomogeneous system, and obtain the following result:Theorem3.2:If (k1+k-1)/(k1+k2+k-1)(?)N, then system (LV) admits a unique polynomial first inte-gral Φ(x)=x1+x2+x3+x4, in the sense of the function independent.