两类具有脉冲控制效应的生态系统动力学问题研究

发布时间：2019-01-19 16:00

【摘要】：本论文主要研究了两类具有脉冲控制效应的生态系统动力学问题,并对相关问题进行深入地研究。论文首先介绍了生态系统动力学问题的研究背景和研究现状,提供了论文研究所需的基本概念以及重要引理等基本知识,它们是后续章节讨论的基础。其次,研究了一类具有脉冲控制效应的扩散生态系统动力学问题。.推导得到了该生态动力学系统解的一致有界性、种群的持久生存性与灭绝性的阈值条件,证明了半平凡周期解的存在性、唯一性和全局渐近稳定性。同时对该生态系统进行了相关动力学数值模拟,模拟结果验证了理论推导定理的有效性与可行性,并进一步揭示了脉冲控制效应对生态系统动力学行为的影响机制。再次,研究了一类具有脉冲控制效应与季节效应的生态系统动力学问题。分析了该生态系统半平凡周期解的存在性、局部渐近稳定性和全局渐近稳定性,讨论了该生态系统种群的灭绝性与持久生存性,建立了相关动力学性质的判定准则。研究结果为进一步研究如何运用脉冲控制策略维持生态种群持久生存提供了一定的理论支撑。最后,对研究结果进行了总结和展望。
[Abstract]:In this paper, two kinds of ecosystem dynamics problems with pulse control effect are studied, and the related problems are studied deeply. Firstly, the background and present situation of ecosystem dynamics are introduced, and the basic concepts and important Lemma are provided, which are the basis of the discussion in the following chapters. Secondly, a kind of diffusion ecosystem dynamics problem with pulse control effect is studied. The threshold conditions for the existence, uniqueness and global asymptotic stability of the semi-trivial periodic solution are obtained. The simulation results verify the validity and feasibility of the theoretical derivation theorem, and further reveal the mechanism of the impulse control effect on the ecosystem dynamics behavior. Thirdly, a class of ecosystem dynamics problems with pulse control and seasonal effects are studied. In this paper, the existence, local asymptotic stability and global asymptotic stability of the semi-trivial periodic solution of the ecosystem are analyzed. The extinction and persistence of the ecosystem population are discussed, and the criteria for determining the dynamic properties of the ecosystem are established. The results provide a theoretical support for further study on how to use impulse control strategy to maintain the sustainable survival of ecological population. Finally, the research results are summarized and prospected.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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