【摘要】：基于銅綠假膿單胞菌群體感應(yīng)機(jī)理及群體感應(yīng)信號(hào)分子具有免疫調(diào)控功能這一生物學(xué)行為,本文研究了幾類銅綠假膿單胞菌群體感應(yīng)對(duì)免疫反應(yīng)影響的數(shù)學(xué)模型的動(dòng)力學(xué)行為,主要討論了模型平衡點(diǎn)的存在性、穩(wěn)定性及分歧行為。第一章主要介紹了銅綠假膿單胞菌及群體感應(yīng)相關(guān)背景知識(shí),銅綠假膿單胞菌群體感應(yīng)數(shù)學(xué)模型的研究進(jìn)展及相關(guān)的理論基礎(chǔ)。第二章建立了一類數(shù)學(xué)模型描述群體感應(yīng)信號(hào)分子的免疫調(diào)控機(jī)理,分析了模型平衡點(diǎn)的存在性及其漸近穩(wěn)定性,并通過(guò)數(shù)值模擬驗(yàn)證了理論結(jié)果的準(zhǔn)確性。有趣的是,我們發(fā)現(xiàn)當(dāng)0 1?(29)1,?(27)1,(35)(29)0時(shí),存在雙穩(wěn)現(xiàn)象。為進(jìn)一步研究雙穩(wěn)態(tài)下平衡點(diǎn)的性質(zhì),通過(guò)構(gòu)造李雅普諾夫函數(shù),對(duì)雙穩(wěn)態(tài)下無(wú)菌平衡點(diǎn)和正平衡點(diǎn)的吸引域進(jìn)行估計(jì),并運(yùn)用Matlab的工具箱GLOPTIPOLY及SeDuMi對(duì)雙穩(wěn)態(tài)下的吸引域進(jìn)行仿真分析。此外,運(yùn)用MatCont分析了模型可能存在的分歧現(xiàn)象,得到了單參數(shù)分歧圖、雙參數(shù)分歧圖。本文的第三章主要研究了一類群體感應(yīng)信號(hào)分子調(diào)控細(xì)菌與免疫系統(tǒng)間競(jìng)爭(zhēng)的數(shù)學(xué)模型,利用Lyapunov方法證明了無(wú)菌平衡點(diǎn)的穩(wěn)定性;分析了正平衡點(diǎn)的存在條件及穩(wěn)定性,并證明了正平衡點(diǎn)前后向分歧的存在性,利用MatCont,通過(guò)數(shù)值模擬進(jìn)一步探測(cè)模型復(fù)雜的動(dòng)力學(xué)行為,得到系統(tǒng)存在的三種動(dòng)力學(xué)性態(tài),包括前、后向分歧以及雙穩(wěn)態(tài)現(xiàn)象。
[Abstract]:Based on the population sensing mechanism of Pseudomonas aeruginosa and the biological behavior of population sensing signaling molecules with immunomodulatory function, the dynamic behaviors of several mathematical models of Pseudomonas aeruginosa group somatosensory response to immune response were studied in this paper. The existence, stability and bifurcation behavior of equilibrium point are discussed. The first chapter mainly introduces the background knowledge of Pseudomonas aeruginosa and its population induction, the research progress of mathematical model of Pseudomonas aeruginosa population induction and the related theoretical basis. In chapter 2, a kind of mathematical model is established to describe the immune regulation mechanism of population sensing signal molecules. The existence and asymptotic stability of the equilibrium point of the model are analyzed, and the accuracy of the theoretical results is verified by numerical simulation. Interestingly, we find that there is bistability when 0? (29) 1? (27) 1, (35) (29) 0. In order to further study the properties of equilibrium point in bistable state, the attractive regions of aseptic equilibrium point and positive equilibrium point in bistable state are estimated by constructing Lyapunov function. Matlab toolbox GLOPTIPOLY and SeDuMi are used to simulate the attraction region in bistable state. In addition, the possible bifurcation phenomena of the model are analyzed by using MatCont, and the single parameter bifurcation graph and the double parameter bifurcation graph are obtained. In the third chapter, a mathematical model of competition between bacteria and immune system is studied, and the stability of aseptic equilibrium point is proved by Lyapunov method. The existence condition and stability of the positive equilibrium point are analyzed, and the existence of the forward and backward bifurcation of the positive equilibrium point is proved. The complex dynamic behavior of the model is further detected by MatCont, numerical simulation, and three dynamic states of the system are obtained. It includes forward, backward bifurcation and bistable phenomena.
【學(xué)位授予單位】：西安科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：R378.991

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