兰州大学机构库 >数学与统计学院
一类三种群捕食者-食饵系统的动力学行为
Alternative TitleDynamical Behavior of a class of Three Species Predator-Prey System
毕志芳
Thesis Advisor林国
2016-05-18
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword稳定性 行波解 上下解 吸引矩形 最小波速
Abstract本文研究三种群捕食者-食饵反应扩散系统。首先研究当区域有界并且满足Neumann边界条件下正平衡点的稳定性。通过使用不变区域可以得到该系统具有非负初值时正平衡点的全局稳定性。其次,讨论无界区域上系统的行波解。利用Schauder不动点定理及构造上下解的方法证明了c>c*时连接平衡点(1,0,0)和正平衡点的非负行波解的存在性,其中,行波解的渐近行为通过利用吸引矩形得到。进一步,利用渐近传播速度的相关结论得出c
Other AbstractThis paper is concerned with the three species predator-prey system. Firstly, we consider the stability of the positive equilibrium on a bounded domain with Neumann condition. We obtain the global stability of the positive equilibrium with non-negative initial-value by using the invariant domain. Secondly, we discuss the traveling wave solutions. By using the Schauder's fixed point theorem and constructing upper and lower solutions, we prove the existence of non-negative traveling wave solutions connecting equilibrium (1,0,0) with positive equilibrium if c>c*, during which the asymptotic behavior of traveling wave solutions is confirmed by using the technique of contracting rectangles. Moreover the nonexistence of traveling wave solutions with c
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224458
Collection数学与统计学院
Recommended Citation
GB/T 7714
毕志芳. 一类三种群捕食者-食饵系统的动力学行为[D]. 兰州. 兰州大学,2016.
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