几类传染病模型和神经网络模型的动力学研究
发布时间：2019-03-27 14:08
【摘要】： 本文主要研究了几类传染病模型和神经网络模型的动力学性质. 全文共分为六章: 第一章介绍了传染病模型、神经网络模型的研究背景及进展,并简单地介绍了本文的主要工作. 第二章研究了一类SEIR模型的正解存在性,分析了解的最终性态,并给出了生物学意义和数值模拟. 第三章研究了一类SEI模型的正解存在性,利用Lyapunov方法分析了平衡点的局部稳定条件和全局指数稳定条件,并阐述了其生物学意义. 第四章研究了一类具有时滞的SEI模型的动力学性质.结合线性化理论和Hopf分支理论,研究了平衡点的稳定性,并以时滞为参数,讨论了该模型的Hopf分支现象,分析了分支方向.最后给出了数值模拟. 第五章利用Kuznetsov讨论离散系统Hopf分支的方法,研究了一类具有三个神经元的离散BAM神经网络模型平衡点的稳定性和Hopf分支现象. 第六章利用推广的Lyapunov方法,研究了一类具有不连续激励函数的时滞Cohen- Grossberg神经网络模型平衡点的全局指数稳定性.
[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.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2008
【分类号】：R181.3
本文编号：2448250
[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.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2008
【分类号】：R181.3
【参考文献】
相关期刊论文 前6条
1 王拉娣;具有非线性传染率的两类传染病模型的全局分析[J];工程数学学报;2005年04期
2 徐文雄,张仲华;具有预防接种免疫力的双线性传染率SIR流行病模型全局稳定性[J];大学数学;2003年06期
3 段文英,魏俊杰,沈启宏;一类具时滞的神经网络模型的Hopf分支[J];数学年刊A辑(中文版);2003年06期
4 刘丽杭,王小万;从发展的角度 深刻认识疾病对社会经济发展的影响[J];中国初级卫生保健;2003年07期
5 曹光,张经坤,张毅,徐昌,柔克明,程颖恺;中国跨世纪的传染病防治[J];中华流行病学杂志;1997年02期
6 曾光;传染性非典型肺炎防制工作中的几个问题[J];中华流行病学杂志;2003年06期
，本文编号：2448250
本文链接：https://www.wllwen.com/yixuelunwen/liuxingb/2448250.html
