兰州大学机构库 >数学与统计学院
周期双稳 Lotka- Volterra 竞争系统的行波解
Alternative TitleTime Periodic Traveling Waves For A Bistable Lotka-Volterra Competition System
包雄雄
Thesis Advisor王智诚
2012-05-27
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword时间周期行波解 双稳~Lotka-Volterra 竞争系统 存在性 唯一性 稳定性
Abstract本文主要研究了时间周期~Lotka-Volterra 竞争系统 \begin{equation*} \begin{cases} u_{t}=u_{xx}+u(r_{1}(t)-a_{1}(t)u-b_{1}(t)v),\\ v_{t}=dv_{xx}+v(r_{2}(t)-a_{2}(t)u-b_{2}(t)v) \end{cases} \end{equation*} 在双稳情形时周期行波解的存在性, 唯一性和渐近稳定性. 首先利用~Fang 和~Zhao \cite{FZ} 中发展的理论建立了连接两个稳定平衡点的周期行波解的存在性, 并且证明了这样的行波解关于空间变量是严格单调的. 进一步, 通过建立辅助系统和上下解, 利用运动平面技术证明了周期行波解在空间平移意义下是唯一存在的. 此后在第四章中利用挤压方法得到了周期行波解是指数渐近稳定的.
Other AbstractIn this paper,we study the existence, uniqueness and asymptotic stability of time traveling wave solutions to a parabolic Lotka-Volterra competition system \begin{equation*} \begin{cases} u_{t}=u_{xx}+u(r_{1}(t)-a_{1}(t)u-b_{1}(t)v),\\ v_{t}=dv_{xx}+v(r_{2}(t)-a_{2}(t)u-b_{2}(t)v). \end{cases} \end{equation*} Under certain conditions, we prove that there exists a wave speed $c$ such that there is a time periodic traveling wave solution connecting two semi-trivial periodic solutions of the corresponding kinetic system. Moreover, we show the uniqueness of traveling wave solution through the sliding method. The stability of traveling wave solution is established by comparison principle, suitably constructed super- and sub-solutions and the method of squeezing in Chapter 4.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224340
Collection数学与统计学院
Recommended Citation
GB/T 7714
包雄雄. 周期双稳 Lotka- Volterra 竞争系统的行波解[D]. 兰州. 兰州大学,2012.
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