变系数两种群Lotka-Volterra方程的通解  

General Solution to the Two Species Lotka-Volterra Equation with Constant Coefficients

作　　者：朱殊洋 朱晏 Zhu Shuyang;Zhu Yan(Research Center of Modern Political Economy,Shanghai University ofFinance and Economics,Shanghai 200433,China;School of Science,Northeast Forestry University,Harbin 150041,China)

机构地区：[1]上海财经大学现代政治经济学数理研究中心,上海200433 [2]东北林业大学理学院,哈尔滨150041

出　　处：《数学理论与应用》2018年第3期43-49,共7页Mathematical Theory and Applications

基　　金：国家自然科学基金项目（No.11501137）资助

摘　　要：二种群Lotka—Volterra方程具有重要的应用价值,采用整体积分法和调整系数法可以求得到该方程的通解.首先进行线性变换,在变换中嵌入未知参数.其次将一个方程代入另一个方程,用整体积分法和调整参数法得到该方程的通解,进而得到另一个方程的通解.最后将这两个解代入原方程即得到二种群Lotka—Volterra方程的通解.The two species Lotka-Volterra equation has important applications.The analytical solution of the equation can be obtained by using the integral method and the adjustment coefficient method.First,a linear transform is carried out and unknown parameters are embedded in the transform.Then the first equation is substituted into the second equation.The analytic solutions of the new equation is obtained by integrating method and parameter adjustment method.Finally,the general solution of the population of two species Lotka-Volterra equation is derived.

关 键 词：二种群Lotka-volterra方程 初等积分法 通解 

分 类 号：O175[理学—数学]