非齐次环境下两种群竞争系统的行波解

发布时间：2017-12-31 06:30

  本文关键词：非齐次环境下两种群竞争系统的行波解　出处：《兰州大学》2016年博士论文　论文类型：学位论文

  更多相关文章： 两种群竞争系统 行波解 时间周期 空间周期 存在性 稳定性

【摘要】：反应扩散系统广泛应用于许多自然科学,包括生物,化学和物理等.行波解是反应扩散方程系统的一种特殊形式的解并且已被广泛用来模拟许多自然现象.特别地,在燃烧理论,化学反应等的实验观察和数值计算中已经发现了许多具有不同形状水平集的行波解.此外,现实的自然环境是随着时间和空间变化而变化的.因此研究非齐次环境下反应扩散方程系统的非平面波具有重要的现实意义.两种群竞争系统是用来模拟两个或多种群相互作用的一类重要模型.本文首先将研究时间周期环境下两种群竞争系统的时间周期非平面行波解.另一方面,非局部扩散发展系统也广泛用于模拟种群在非邻近区域的相互作用.本文也将研究具有非局部扩散的两种群竞争系统在空间周期环境下的空间周期行波解.本文首先研究了时间周期的两种群扩散系统在二维空间中的时间周期V形行波解.为此,本文建立了系统一维时间周期行波解在无穷远处的渐近行为.然后通过构造适当的上下解,证明时间周期的二维曲面行波解的存在性.进一步,我们证明了时间周期曲面行波解是渐近稳定并唯一的.其次研究了时间周期两种群扩散系统在高维空间RN(N≥3)中的时间周期棱锥形行波解.利用比较原理并构造适当的上下解,证明了在RN中时间周期两种群扩散系统存在时间周期棱锥形行波解并给出了时间周期棱锥形行波解所满足的定性性质.最后研究了具有非局部扩散的两种群争系统在空间周期环境下的空间周期行波解.在适当的假设下,系统存在两个空间周期的半平凡平衡解(u*1(x),0)和(0,u*2(x)),其中(u*1(x),0)是线性并全局渐近稳定的而(0,u*2(x))在空间周期扰动下是线性不稳定的.利用上下解技术和比较原理,对每个ξ∈SN-1,证明系统存在连接(u*1(x),0)和(0,u*2(x))并在ξ方向以波速cc*(ξ)传播的空间周期行波解,其中c*(ξ)是系统在ξ方向的传播速度.另外,对cc*(ξ),系统不存在这样的行波解.当波速cc*(ξ),利用挤压方法也证明了空间周期行波解的渐近稳定性和唯一性.
[Abstract]:Reaction-diffusion systems are widely used in many natural sciences, including biology. The traveling wave solution is a special form of solution of the reaction-diffusion equation system and has been widely used to simulate many natural phenomena, especially in the combustion theory. Many traveling wave solutions with different shape horizontal sets have been found in the experimental observation and numerical calculation of chemical reactions. The natural environment of reality changes with time and space. Therefore, it is of great practical significance to study the nonplane wave of the reaction-diffusion equation system in a non-homogeneous environment. The two-species competition system is used to simulate two or two species. In this paper, we first study the time-periodic nonplanar traveling wave solutions of a two-species competitive system in a time-periodic environment. Non-local diffusion development systems are also widely used to simulate the interaction of populations in non-adjacent regions. In this paper, we will also study the spatial periodic traveling wave solutions of two species competitive systems with non-local diffusion in spatial periodic environment. In this paper, the time-periodic V-shaped traveling wave solutions of a time-periodic two-species diffusion system in two-dimensional space are studied. In this paper, the asymptotic behavior of one-dimensional time-periodic traveling wave solutions at infinity is established, and then the existence of time-periodic two-dimensional surface traveling wave solutions is proved by constructing appropriate upper and lower solutions. We prove that the traveling wave solution of time-periodic surface is asymptotically stable and unique. Secondly, we study the time-periodic two-species diffusion system with RN(N 鈮，

本文编号：1358596