一个具有毒性效应的营养—浮游植物反应扩散模型的研究

发布时间：2018-04-06 22:39

  本文选题：有毒性效应的营养-浮游植物反应扩散模型　切入点：稳定性　出处：《江苏师范大学》2017年硕士论文

【摘要】：近年来反应扩散方程的研究日益受到重视,反应扩散方程涉及的大量问题来自物理学,化学和生物学中众多的数学模型,从而有强烈的实际背景.对生物学中的营养-浮游植物模型模型进行研究,不仅具有重大的理论意义,也具有很大的实用价值.Chakraborty等人提出了一个复杂的营养-浮游植物模型,研究结果表明系统的渐近稳定性和图灵不稳定性依赖于毒性效应θ[9].θ提高时,则会出现图灵不稳定.本文主要研究了一个简单的具有毒性效应的营养-浮游植物模型,通过运用比较原理,偏微分定理中的能量估计,隐函数定理等方法更好地研究解的定性性质.主要研究内容如下:第一章对营养-浮游植物模型的研究背景和意义做了介绍,并简单的介绍了本文的主要工作.第二章研究了其反应扩散方程的解的先验估计和长时间渐近行为,并讨论了抛物系统的吸引子的存在性第三章关心的是对应的椭圆型方程的常数解的稳定性,特别是图灵不稳定性.第四章致力于对椭圆型方程的解进行先验估计,将是讨论非常数稳态解的不存在性和存在性的基础.在第五章和第六章中,主要分析了当扩散系数在一定范围内变化时,椭圆方程的非常数解的存在性与不存在性,分别运用了能量估计,隐函数定理和Leray-Schauder拓扑度对其进行讨论.第七章总结了本论文的研究结果,并与提出的具有Holling-Ⅲ型功能反应的毒性效应的模型进行比较[9].
[Abstract]:In recent years, more and more attention has been paid to the study of the reaction diffusion equation. A large number of problems related to the reaction diffusion equation come from many mathematical models in physics, chemistry and biology, so it has a strong practical background.The study of nutrition-phytoplankton model in biology is not only of great theoretical significance, but also of great practical value. Chakraborty et al put forward a complex nutrition-phytoplankton model.The results show that the asymptotic stability and Turing instability of the system depend on the toxic effect 胃 [9]. When 胃 increases, Turing instability will occur.In this paper, a simple nutrition-phytoplankton model with toxic effect is studied. By using the comparison principle, the energy estimation in the partial differential theorem and the implicit function theorem, the qualitative properties of the solution are better studied.The main contents are as follows: the first chapter introduces the background and significance of nutrition-phytoplankton model, and briefly introduces the main work of this paper.In chapter 2, we study the priori estimation and long-time asymptotic behavior of the solution of the reaction-diffusion equation, and discuss the existence of the attractor of the parabolic system. In Chapter 3, we focus on the stability of the constant solution of the corresponding elliptic equation.Especially Turing instability.In chapter 4, a priori estimate of the solutions of elliptic equations is proposed, which will be the basis for discussing the nonexistence and existence of the steady-state solutions of non-constant numbers.In the fifth and sixth chapters, the existence and non-existence of the nonconstant solutions of the elliptic equation are analyzed when the diffusion coefficient varies within a certain range. The energy estimation, implicit function theorem and Leray-Schauder topological degree are used to discuss the existence and non-existence of the solutions respectively.In chapter 7, the results of this paper are summarized and compared with the proposed model with the toxic effect of Holling- 鈪，

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