具有交叉扩散项的两种群Lotka-Volterra模型的对称分类和稳定性分析  

Stability Analysis and Symmetry Classification for a 2-Species Lotka-Volterra Model with Cross-diffusion

作　　者：李吉娜[1] 姬雪晖 王雪柯 LI Jina;JI Xuehui;WANG Xueke(College of Science,Zhongyuan University of Technology,Zhengzhou 450007,China)

机构地区：[1]中原工学院理学院,河南郑州450007

出　　处：《应用数学》2021年第4期863-869,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China under Grant(11701594, 11947093);Training Plan for Key Young Teachers of Colleges and Universities in Henan Province (2019GGJS143);Key Research Projects of Henan Higher Education Institutions (21A110026)。

摘　　要：本文主要研究具有交叉扩散项的两种群Lotka-Volterra模型.首先利用广义条件对称方法研究该模型的对称约化和对称分类问题,并将分类后的方程约化为常微分方程组.最后,通过两个例子得到Lotka-Volterra模型的解并分析其稳定性.This paper studies a 2-species Lotka-Volterra model with cross-diffusion. The symmetry classification and symmetry reduction of the Lotka-Volterra model are considered by the generalized conditional symmetry. Then, the resulting Lotka-Volterra equations can be reduced to a system of ordinary differential equations. At last, the stability analysis and solutions of the Lotka-Volterra system are shown by two examples.

关 键 词：对称分类 对称约化 LOTKA-VOLTERRA模型 稳定性分析 

分 类 号：O175.2[理学—数学]