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

LI Jina(李吉娜),JI Xuehui(姬雪晖),WANG Xueke(王雪柯)

(College of Science,Zhongyuan University of Technology,Zhengzhou 450007,China)

Abstract: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.

Key words:Symmetry classification;Symmetry reduction;Lotka-Volterra model;Stability analysis

1.Introduction

2.Symmetry Classification of the System(1.1)

3.Reduction Examples