带时滞的肿瘤模型的稳定性及Hopf分岔分析

发布时间：2018-03-21 16:13

本文选题：肿瘤生长　切入点：病毒疗法　出处：《云南师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：癌症作为威胁人类健康的头号杀手,已经成为全球人都关心的热门话题.近年来,科学家们运用数学方法对肿瘤模型的动力学性质进行研究.本文运用微分方程分岔理论研究带时滞的肿瘤生长模型和肿瘤病毒疗法模型.研究的主要内容如下:一、介绍了国内外在肿瘤生长方面的发展和研究现状,分析并研究了具有两个时滞的肿瘤生长模型.首先,通过讨论系统线性化近似方程的特征方程根的分布情况,选取τ_1,τ_2作为分岔参数,研究了系统的稳定性;然后,运用Hopf分岔理论,分析了Hopf分岔的存在性;其次,运用规范型理论和中心流形定理方法,给出了判断分岔方向和分岔周期解稳定性的量的计算公式;最后,运用数学软件Mathematica进行了数值模拟.二、介绍了国内外在肿瘤病毒疗法方面的发展和研究现状,运用相同的方法,分析并研究了具有两个时滞的肿瘤病毒疗法模型的动力学性质。
[Abstract]:Cancer, as the number one killer threatening human health, has become a hot topic of global concern. Scientists use mathematical methods to study the dynamic properties of tumor models. In this paper, differential equation bifurcation theory is used to study tumor growth model with delay and tumor virus therapy model. The main contents of this study are as follows: 1. This paper introduces the development and research status of tumor growth at home and abroad, and analyzes and studies the tumor growth model with two delays. Firstly, the distribution of characteristic equation roots of the linearized approximate equation of the system is discussed. The stability of the system is studied by selecting 蟿 _ T _ 1 and 蟿 _ 2 as bifurcation parameters. Then, the existence of Hopf bifurcation is analyzed by using Hopf bifurcation theory. Secondly, the normal form theory and the method of center manifold theorem are used to study the stability of the system. The calculation formulas for judging the bifurcation direction and the stability of bifurcation periodic solution are given. Finally, numerical simulation is carried out by using the mathematical software Mathematica. Secondly, the development and research status of tumor virus therapy at home and abroad are introduced. The dynamic properties of a tumor virus therapy model with two delays are analyzed and studied by the same method.
【学位授予单位】：云南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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