本文選題：恒化器模型　切入點(diǎn)：全局吸引　出處：《新疆大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：恒化器(Chemostat)是一款用于微生物培養(yǎng)的主要實(shí)驗(yàn)裝置.利用該裝置研究的微生物培養(yǎng)模型展示了系統(tǒng)持久性、滅絕性及平衡點(diǎn)的存在性等動力學(xué)行為,給人工培養(yǎng)有益微生物和消滅有害微生物提供了理論依據(jù)和科學(xué)指導(dǎo).此外,浮游生物作為水域中食物鏈的底層,研究關(guān)于浮游生物的恒化器模型有著重要的生態(tài)意義.近幾年,關(guān)于恒化器的模型被許多學(xué)者討論過,并取得了非常重要的研究成果.在這些模型的啟發(fā)下,本文主要考慮了以下三種模型,具有營養(yǎng)循環(huán)和收獲的脈沖Chemostat模型研究,具有脈沖和收獲的時滯Chemostat模型研究,具有休眠和時滯的浮游生物-營養(yǎng)相互作用模型研究.主要利用脈沖微分方程的比較原理直接得出以上系統(tǒng)持久和滅絕的充分條件.本文的主要內(nèi)容可總結(jié)如下:第1節(jié)為引言,介紹了具有脈沖和收獲的Chemostat模型的研究背景、目的和意義,并給出了目前具有脈沖和收獲的Chemostat模型的研究現(xiàn)狀和成果,在最后部分呈現(xiàn)本文的組織框架.第2節(jié)為預(yù)備知識,總結(jié)了本文模型研究所需的基本引理,并給于證明過程.第3節(jié)主要探討了一類營養(yǎng)循環(huán)和收獲的脈沖Chemostat模型,利用脈沖微分方程的比較原理和Floquet理論,得出了微生物滅亡周期解的全局吸引性和系統(tǒng)持久的充分條件,最后用數(shù)值模擬,驗(yàn)證了系統(tǒng)研究結(jié)果的準(zhǔn)確性.第4節(jié)主要利用脈沖時滯微分方程的比較原理得出了一類具有脈沖和收獲的時滯Chemostat模型的閾值,利用這個閾值解討論了微生物滅亡周期解的全局吸引性和系統(tǒng)持久的充分條件,最后給出兩個例子驗(yàn)證結(jié)論的有效性.第5節(jié)中,我們討論了一類具有休眠和時滯的浮游生物-營養(yǎng)相互作用模型.系統(tǒng)討論了模型的持久性和滅絕性,揭示了在脈沖擾動的情況下時滯對系統(tǒng)的重要影響.
[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.
【學(xué)位授予單位】：新疆大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 賈建文;張紅紅;;具有增長時滯及脈沖輸入的被污染Beddington-DeAngelis恒化器模型的分析[J];應(yīng)用數(shù)學(xué);2010年03期

，

本文編號：1599038