競爭系統的收斂區域

Abstract

本論文是研究競爭模式中的兩個系統, 其一為不具擴散作用的動力系統, 另者為具擴散作用的穩定系統.我們考慮此系統的非常數共存解的存在性 與收斂區域, 先作線性穩定性分析再求其數值解. In this thesis our goal is to study the two syatems of Lotka- Volterra-Gause Competition Model. One is dynamical system without diffusion, and the other is steady state system with diffusion. We dicuss the stabilities of their equilibrium. We consider existence of non-constant coexitence solutions and domain of attraction. We first analyze this system by linear stability analysis to find the local stability. Then, we use Taylor expansion to obtain numerical solutions.