具有脉冲和收获的Chemostat模型研究

发布时间：2018-03-11 16:48

本文选题：恒化器模型　切入点：全局吸引　出处：《新疆大学》2017年硕士论文　论文类型：学位论文

【摘要】：恒化器(Chemostat)是一款用于微生物培养的主要实验装置.利用该装置研究的微生物培养模型展示了系统持久性、灭绝性及平衡点的存在性等动力学行为,给人工培养有益微生物和消灭有害微生物提供了理论依据和科学指导.此外,浮游生物作为水域中食物链的底层,研究关于浮游生物的恒化器模型有着重要的生态意义.近几年,关于恒化器的模型被许多学者讨论过,并取得了非常重要的研究成果.在这些模型的启发下,本文主要考虑了以下三种模型,具有营养循环和收获的脉冲Chemostat模型研究,具有脉冲和收获的时滞Chemostat模型研究,具有休眠和时滞的浮游生物-营养相互作用模型研究.主要利用脉冲微分方程的比较原理直接得出以上系统持久和灭绝的充分条件.本文的主要内容可总结如下:第1节为引言,介绍了具有脉冲和收获的Chemostat模型的研究背景、目的和意义,并给出了目前具有脉冲和收获的Chemostat模型的研究现状和成果,在最后部分呈现本文的组织框架.第2节为预备知识,总结了本文模型研究所需的基本引理,并给于证明过程.第3节主要探讨了一类营养循环和收获的脉冲Chemostat模型,利用脉冲微分方程的比较原理和Floquet理论,得出了微生物灭亡周期解的全局吸引性和系统持久的充分条件,最后用数值模拟,验证了系统研究结果的准确性.第4节主要利用脉冲时滞微分方程的比较原理得出了一类具有脉冲和收获的时滞Chemostat模型的阈值,利用这个阈值解讨论了微生物灭亡周期解的全局吸引性和系统持久的充分条件,最后给出两个例子验证结论的有效性.第5节中,我们讨论了一类具有休眠和时滞的浮游生物-营养相互作用模型.系统讨论了模型的持久性和灭绝性,揭示了在脉冲扰动的情况下时滞对系统的重要影响.
[Abstract]:Chemostata is a main experimental device used in microbial culture. The model of microorganism culture studied by this device shows the dynamic behavior of system persistence, extinction and existence of equilibrium point. It provides theoretical basis and scientific guidance for the artificial cultivation of beneficial microorganisms and the elimination of harmful microbes. In addition, plankton serves as the bottom of the food chain in the waters. It is of great ecological significance to study the model of the chemostat on plankton. In recent years, many scholars have discussed the model of the chemostat, and obtained very important research results. In this paper, the following three models are considered: pulse Chemostat model with nutrient cycle and harvest, delay Chemostat model with pulse and harvest. The study of plankton nutrient interaction model with dormancy and delay. The sufficient conditions for the persistence and extinction of the above system are obtained directly by using the comparison principle of impulsive differential equations. The main contents of this paper can be summarized as follows. Section 1 is an introduction, This paper introduces the research background, purpose and significance of Chemostat model with pulse and harvest, and gives the research status and achievements of Chemostat model with pulse and harvest. In the last part, the organizational framework of this paper is presented. This paper summarizes the basic Lemma needed for the study of the model and gives the proof process. Section 3 mainly discusses a class of impulsive Chemostat models for nutrient cycling and harvesting, using the comparison principle of impulsive differential equations and Floquet theory. The sufficient conditions for the global attractiveness of the periodic solution of microbial extinction and the persistence of the system are obtained. Finally, the numerical simulation is carried out. In section 4, by using the comparison principle of impulsive delay differential equations, the threshold of a class of delay Chemostat models with impulses and harvests is obtained. By using this threshold solution, the sufficient conditions for the global attractiveness of the periodic solution of microbial extinction and the persistence of the system are discussed. Finally, two examples are given to verify the validity of the conclusion. In this paper, we discuss a class of plankton nutrient interaction models with dormancy and delay, discuss the persistence and extinction of the model, and reveal the important influence of time delay on the system under the condition of impulsive disturbance.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【参考文献】