【摘要】：基于銅綠假膿單胞菌群體感應機理及群體感應信號分子具有免疫調(diào)控功能這一生物學行為,本文研究了幾類銅綠假膿單胞菌群體感應對免疫反應影響的數(shù)學模型的動力學行為,主要討論了模型平衡點的存在性、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相關背景知識,銅綠假膿單胞菌群體感應數(shù)學模型的研究進展及相關的理論基礎。第二章建立了一類數(shù)學模型描述群體感應信號分子的免疫調(diào)控機理,分析了模型平衡點的存在性及其漸近穩(wěn)定性,并通過數(shù)值模擬驗證了理論結(jié)果的準確性。有趣的是,我們發(fā)現(xiàn)當0 1?(29)1,?(27)1,(35)(29)0時,存在雙穩(wěn)現(xiàn)象。為進一步研究雙穩(wěn)態(tài)下平衡點的性質(zhì),通過構(gòu)造李雅普諾夫函數(shù),對雙穩(wěn)態(tài)下無菌平衡點和正平衡點的吸引域進行估計,并運用Matlab的工具箱GLOPTIPOLY及SeDuMi對雙穩(wěn)態(tài)下的吸引域進行仿真分析。此外,運用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信號分子調(diào)控細菌與免疫系統(tǒng)間競爭的數(shù)學模型,利用Lyapunov方法證明了無菌平衡點的穩(wěn)定性;分析了正平衡點的存在條件及穩(wěn)定性,并證明了正平衡點前后向分歧的存在性,利用MatCont,通過數(shù)值模擬進一步探測模型復雜的動力學行為,得到系統(tǒng)存在的三種動力學性態(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.
【學位授予單位】：西安科技大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：R378.991

【參考文獻】

相關期刊論文 前8條

1 張仲華;孟慶勛;鎖要紅;;一類具有病菌信息交流機制的時滯模型的穩(wěn)定性[J];上海大學學報(自然科學版);2013年03期

2 衛(wèi)陽;張亞妮;段康民;;銅綠假單胞菌鐵與群體感應系統(tǒng)的調(diào)節(jié)[J];西北大學學報(自然科學版);2010年05期

3 梁海華;沈立新;馬艷玲;段康民;;銅綠假單胞菌中群體感應系統(tǒng)研究進展[J];微生物學通報;2010年07期

4 張仲華;鎖要紅;;一類具有群體感應機理的傳染病模型漸近分析[J];紡織高校基礎科學學報;2009年03期

5 李曼;邱健;宋水山;;真菌中的群體感應系統(tǒng)[J];微生物學通報;2007年03期

6 劉鵬;張月娟;趙廷昌;;細菌群體感應系統(tǒng)的研究進展[J];中國農(nóng)學通報;2007年06期

7 徐凱進;李蘭娟;邢卉春;吳仲文;俞云松;盛吉芳;陳亞崗;;細菌的群體感應系統(tǒng)[J];中華傳染病雜志;2006年05期

8 李承光;賈振華;邱健;張霞;馬宏;冀營光;宋水山;;細菌群體感應系統(tǒng)研究進展及其應用[J];生物技術通報;2006年01期

相關碩士學位論文 前1條

1 王秀男;HIV感染動力學模型分析[D];西南大學;2013年

，

本文編號：2305266