具有两种年龄结构单种群模型的行波解

发布时间：2019-05-10 01:26

【摘要】：众所周知,种群生态学作为数学在生态学中应用最为广泛和成熟的分支之一.许多种群模型的研究都可归结为对反应扩散方程的研究,在研究种群的扩散现象时,大多数种群受到时变环境的影响,动力学行为发生很大的变化,比如就季节而言:不同季节,由于温度高低和食物供给问题,种群的出生率,死亡率和扩散率随之改变.因此,研究时变环境对种群模型的影响具有重要的理论和实际意义.本文考虑了在时变环境的影响下,具有两种年龄结构和分布成熟时滞的非局部扩散单种群模型行波解的存在性,通过傅立叶变换得到具有两种年龄结构和分布成熟时滞的非局部扩散单种群模型,研究了该模型的初值问题并建立了比较原理,构造合适的上下解并应用上下解方法,证明了行波解的存在性.在空间离散的斑块环境中,格动力系统被用来描述种群的增长和入侵过程,并且种群的生活环境一般都在二维空间上,因此考虑在二维空间上,受时变环境的影响,具有两种年龄结构和分布成熟时滞单种群模型的行波解.首先通过二维离散傅立叶变换得到具有两种年龄结构和分布成熟时滞的单种群模型,然后通过构造适当的上下解并建立比较原理,证明了行波解的存在性和唯一性.
[Abstract]:As we all know, population ecology is one of the most widely used and mature branches of mathematics in ecology. The study of many population models can be summed up as the study of reaction-diffusion equation. When studying the diffusion phenomenon of population, most populations are affected by time-varying environment, and the dynamic behavior has changed greatly. For example, as far as the season is concerned: in different seasons, the birth rate, mortality rate and diffusion rate of the population change due to the problems of temperature and food supply. Therefore, it is of great theoretical and practical significance to study the influence of time-varying environment on population model. In this paper, we consider the existence of traveling wave solutions for nonlocally diffused single population models with two age structures and distributed maturity delays under the influence of time-varying environments. A nonlocal diffusion single population model with two age structures and distributed maturity delays is obtained by Fourier transform. the initial value problem of the model is studied and the comparison principle is established. The appropriate upper and lower solutions are constructed and the upper and lower solutions are applied. The existence of traveling wave solutions is proved. In the spatial discrete patch environment, the lattice dynamic system is used to describe the growth and invasion process of the population, and the living environment of the population is generally in the two-dimensional space, so it is considered that in the two-dimensional space, it is affected by the time-varying environment. Traveling wave solutions of a single population model with two age structures and distributed maturity delays. Firstly, a single population model with two age structures and distributed maturity delays is obtained by two-dimensional discrete Fourier transform, and then the existence and uniqueness of traveling wave solutions are proved by constructing appropriate upper and lower solutions and establishing comparison principles.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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