A Numerical Study of Several Species Population Models  

作　　者：Francisco J. Sánchez-Bernabe Maria del Rosario Escalona-Magdaleno Francisco J. Sánchez-Bernabe;Maria del Rosario Escalona-Magdaleno(Department of Mathematics, Universidad Autónoma Metropolitana Iztapalapa, Ciudad de México, Mexico;Instituto de Educación Media Superior de la Ciudad de México, Plantel Miravalle, Zapote y Mirador, Mexico)

机构地区：[1]Department of Mathematics, Universidad Autónoma Metropolitana Iztapalapa, Ciudad de México, Mexico [2]Instituto de Educación Media Superior de la Ciudad de México, Plantel Miravalle, Zapote y Mirador, Mexico

出　　处：《Journal of Applied Mathematics and Physics》2023年第12期3943-3952,共10页应用数学与应用物理(英文)

摘　　要：This work considers a special case of Lotka-Volterra equations, which means that in the system of two ordinary differential equations, we take the four parameters equal to one. The reason is that we want just to illustrate the procedure to reduce that system to only one ordinary differential equation, such that we know its analytical solution. This idea will be applied to study the relations between a system of three ordinary differential equations, and a couple of partial differential equations. Lotka-Volterra equations are solved numerically by a fourth-order predictor-corrector method, which is initialized by an improved Euler method with a rather small time step because it is only a second-order algorithm. Then, it is proposed a model with three species, defined by ordinary differential equations.This work considers a special case of Lotka-Volterra equations, which means that in the system of two ordinary differential equations, we take the four parameters equal to one. The reason is that we want just to illustrate the procedure to reduce that system to only one ordinary differential equation, such that we know its analytical solution. This idea will be applied to study the relations between a system of three ordinary differential equations, and a couple of partial differential equations. Lotka-Volterra equations are solved numerically by a fourth-order predictor-corrector method, which is initialized by an improved Euler method with a rather small time step because it is only a second-order algorithm. Then, it is proposed a model with three species, defined by ordinary differential equations.

关 键 词：Lotka-Volterra Equations Adams-Bashfort Predictor Adams-Moulton Corrector Improved Euler Method GeoGebra Matlab 

分 类 号：O17[理学—数学]