几类浮游生物生态系统的扩散和时滞动力学机理

发布时间：2018-06-07 21:24

本文选题：扩散 + 时滞　；参考：《温州大学》2016年硕士论文

【摘要】：水体富营养化引起的赤潮和水华等生态灾害问题受到广泛的关注,其产生的机理成为国内外研究热点问题之一。本论文基于泛函微分方程、偏微分方程和水域生态学等相关理论知识,探讨了几类浮游生物生态系统的扩散和时滞动力学机理。本文首先构建了一类浮游植物-浮游动物生态系统,研究其扩散动力学机理。主要分析了生态系统正平衡点的存在性和稳定性、Hopf分支的存在性和发生图灵失稳的临界条件,这些理论推导工作为后续相关动力学模拟提供了理论指导。数值模拟结果验证了理论分析的正确性和可行性,并进一步说明了该生态系统具有复杂的扩散动力学机制。其次,解析了具有Holling-type II和Beddington-DeAngelis功能反应项的浮游植物-浮游动物生态系统的扩散动力学机制。主要探究了生态系统平衡点的局部和全局渐近稳定性,推导出浮游植物种群和两类浮游动物种群可以共存的临界条件,并进一步探究出该生态系统存在非常数稳态解的关键条件。此外,分析结果表明:该生态系统在没有考虑扩散因素的条件下,其正平衡点是局部渐近稳定的;而在考虑扩散因素时,这个平衡点将变为不稳定,继而该生态系统产生非常数稳态解。最后,研究了一类营养盐-浮游植物-浮游动物生态系统的时滞动力学机理。基于中心流形定理和泛函微分方程理论,推导出生态系统正平衡点的稳定性和Hopf分支存在性。理论结果表明时滞对生态系统正平衡点稳态转换具有重要影响。数值模拟结果表明该生态系统正平衡点稳态转换次数是可求的。同时,以时滞为控制变量,模拟生态系统动力学性态演化进程,结果表明时滞对生态系统的动力学性态具有强烈的影响机理。
[Abstract]:The ecological disasters such as red tide and Shui Hua caused by eutrophication of water have been paid more and more attention, and its mechanism has become one of the hot research topics at home and abroad. Based on functional differential equations, partial differential equations and water ecology, the diffusion and time-delay dynamics of several plankton ecosystems are discussed in this paper. In this paper, a class of phytoplankton zooplankton ecosystem was constructed and its diffusion dynamics was studied. The existence and stability of the positive equilibrium point of ecosystem and the existence of Hopf bifurcation and the critical conditions for Turing instability are analyzed. These theoretical deductions provide theoretical guidance for the subsequent dynamic simulation. The numerical simulation results verify the correctness and feasibility of the theoretical analysis and further illustrate the complex diffusion dynamics mechanism of the ecosystem. Secondly, the diffusion dynamics of phytoplankton zooplankton ecosystem with Holling-type II and Beddington-DeAngelis functional response terms were analyzed. In this paper, the local and global asymptotic stability of the equilibrium point of ecosystem is studied, and the critical conditions for the coexistence of phytoplankton population and two species of zooplankton populations are derived. Furthermore, the key conditions for the existence of non-constant steady-state solutions in the ecosystem are further explored. In addition, the results show that the positive equilibrium point of the ecosystem is locally asymptotically stable without considering the diffusion factor, and the equilibrium point becomes unstable when the diffusion factor is considered. In turn, the ecosystem produces a non-constant number of steady-state solutions. Finally, the delay dynamic mechanism of a class of nutrient-phytoplankton-zooplankton ecosystem is studied. Based on the central manifold theorem and the theory of functional differential equations, the stability and Hopf bifurcation of positive equilibrium point of ecosystem are derived. The theoretical results show that the time-delay has an important effect on the steady state transition of the positive equilibrium point of the ecosystem. The numerical simulation results show that the number of steady-state transitions of the positive equilibrium point of the ecosystem can be obtained. At the same time, time delay is used as control variable to simulate the evolution process of ecosystem dynamics. The results show that time delay has a strong influence mechanism on ecosystem dynamics.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175

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