一类三种群捕食者-食饵系统的动力学行为

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 Title	Dynamical 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 Abstract	This 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
Identifier	https://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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