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题名 具年龄结构和分布时滞的竞争生态模型的行波解的存在性
姓名 王仁虎
院系 数学与统计学院
专业 应用数学
学位名称 理学硕士
外文题名 Existence of traveling waves in Lotka-Volterra competition models with stage structure and distributed maturation delay
第一导师姓名 李万同
关键词 时滞;非局部;反应扩散;行波解;竞争;年龄结构
外文关键词 Time-delay;Nonlocal;Reaction-Diffusion;Traveling Waves;Competitive;Stage-structured
学科 理学
摘要 本文对一类具有阶段结构和分布成熟时滞的L-V 型竞争模型首先研究了平衡 点的稳定性,进一步当不存在共存平衡点时考察了连接两个边界平衡点的行波解的 存在性。连接两个边界平衡点的行波解具有重要的生态学意义,它表示了在一个只 有弱竞争的物种栖息的环境中,一个强竞争的物种被引入,进而入侵并控制该区域, 最终导致弱竞争物种在该区域灭绝而仅剩强竞争物种在该区域生存。本文考虑了两 种情况:在第二章中,研究了幼体不扩散(在空间中不走动)的情况;在第三章中, 研究了幼体扩散(即在空间中走动)并且具有收获项的情况。平衡点的稳定性是通 过讨论该平衡点处的线性化方程的特征值得到的,而行波解的存在性是利用单调迭 代和上下解方法建立的。本文的结果拓展了以前的相应结果。 关键词: 时滞, 非局部, 反应扩散, 行波解, 竞争, 年龄结构
外文摘要 This paper is concerned with a Lotka-Volterra competition model with stage structure and distributed maturation delays. The stability of uniform steady states are ¯rstly studied by investigating the eigenvalues of the linearization in every equi- librium and then, the existence of traveling wave solutions connecting two boundary equilibriums is established by using monotone iteration together with upper and lower solutions method when the coexistence equilibrium is absence. The traveling wave solutions represent that some of the stronger competitor of two comptitors are introduced and then invade and dominate an environment, where only the weaker competitor initially inhabit, and drive the weaker to extinction so that the end re- sult is that only the stronger species is present. Two cases are considered in this paper: One of cases is that the immatures do not move in spatial, which is studied in Chapter 2, and another case is that the immatures move in spatial while harvesting e®ect is introduced, which is studied in Chapter 3. The results presented in this paper expand a number of existing ones. Key Words: Time-delay, Nonlocal, Reaction-Di®usion, Traveling Waves, Compet- itive, Stage-structured
研究领域 微分方程理论及应用
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