变系数两种群Lotka-Volterra方程的通解

数学理论与应用 ›› 2018, Vol. 38 ›› Issue (3-4): 43-49.

变系数两种群Lotka-Volterra方程的通解

朱殊洋¹，朱晏²

1.上海财经大学现代政治经济学数理研究中心;
2.东北林业大学理学院

出版日期:2018-12-30 发布日期:2020-09-21

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

Online:2018-12-30 Published:2020-09-21
Supported by:
国家自然科学基金项目(No.11501137)

摘要/Abstract

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.

关键词: 二种群, Lotka—volterra方程 , 初等积分法, 通解

Abstract: 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.

Key words: Two species , Lotka—volterra equation, Elementary integral method, General solution

朱殊洋, 朱晏. 变系数两种群Lotka-Volterra方程的通解[J]. 数学理论与应用, 2018, 38(3-4): 43-49.

Zhu Shuyang, Zhu Yan. General Solution to the Two Species Lotka—Volterra Equation with Constant Coefficients[J]. Mathematical Theory and Applications, 2018, 38(3-4): 43-49.