發(fā)布時間：2019-03-27 14:08

【摘要】： 本文主要研究了幾類傳染病模型和神經(jīng)網(wǎng)絡(luò)模型的動力學(xué)性質(zhì). 全文共分為六章: 第一章介紹了傳染病模型、神經(jīng)網(wǎng)絡(luò)模型的研究背景及進展,并簡單地介紹了本文的主要工作. 第二章研究了一類SEIR模型的正解存在性,分析了解的最終性態(tài),并給出了生物學(xué)意義和數(shù)值模擬. 第三章研究了一類SEI模型的正解存在性,利用Lyapunov方法分析了平衡點的局部穩(wěn)定條件和全局指數(shù)穩(wěn)定條件,并闡述了其生物學(xué)意義. 第四章研究了一類具有時滯的SEI模型的動力學(xué)性質(zhì).結(jié)合線性化理論和Hopf分支理論,研究了平衡點的穩(wěn)定性,并以時滯為參數(shù),討論了該模型的Hopf分支現(xiàn)象,分析了分支方向.最后給出了數(shù)值模擬. 第五章利用Kuznetsov討論離散系統(tǒng)Hopf分支的方法,研究了一類具有三個神經(jīng)元的離散BAM神經(jīng)網(wǎng)絡(luò)模型平衡點的穩(wěn)定性和Hopf分支現(xiàn)象. 第六章利用推廣的Lyapunov方法,研究了一類具有不連續(xù)激勵函數(shù)的時滯Cohen- Grossberg神經(jīng)網(wǎng)絡(luò)模型平衡點的全局指數(shù)穩(wěn)定性.
[Abstract]:In this paper, the dynamical properties of several infectious disease models and neural network models are studied. The thesis is divided into six chapters: the first chapter introduces the research background and progress of infectious disease model, neural network model, and briefly introduces the main work of this paper. In chapter 2, the existence of positive solution for a class of SEIR model is studied, and the final behavior of the solution is analyzed, and the biological significance and numerical simulation are given. In chapter 3, the existence of positive solutions for a class of SEI models is studied. The local stability conditions and global exponential stability conditions of the equilibrium point are analyzed by using the Lyapunov method, and their biological significance is expounded. In chapter 4, the dynamic properties of a class of SEI model with time delay are studied. Based on the linearization theory and the Hopf bifurcation theory, the stability of the equilibrium point is studied. The Hopf bifurcation phenomenon of the model is discussed and the direction of bifurcation is analyzed by taking the time delay as the parameter. Finally, the numerical simulation is given. In chapter 5, the stability of equilibrium point and the phenomenon of Hopf bifurcation of a discrete BAM neural network model with three neurons are studied by using the method of Kuznetsov to discuss the Hopf bifurcation of discrete systems. In chapter 6, the global exponential stability of equilibrium points for a class of delayed Cohen- Grossberg neural networks with discontinuous excitation functions is studied by using the generalized Lyapunov method.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2008
【分類號】：R181.3

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