离散寄生虫—宿主模型的动力学分析
发布时间：2019-05-03 19:51
【摘要】：本文主要研究了一类简单的离散寄生虫-宿主模型的动力学特性,分为如下三个章节进行讨论:第一章首先介绍了本文的选题意义、研究背景及研究现状.第二章介绍了研究模型动力学性质的相关预备知识即与模型有关的分岔理论、中心流形定理和Marotto意义下的混沌,并介绍了论文的主要工作.第三章用Euler方法将连续的寄生虫-宿主模型离散化,研究离散模型的动力学性质.首先,讨论了不动点的存在性和稳定性,应用中心流形定理和分岔理论得到了系统发生Flip分岔和Neimark-Sacker分岔的条件.其次,根据Marotto混沌的定义证明了存在Marotto意义下的混沌.数值模拟验证了理论结果,并发现此系统具有丰富复杂的动力学行为(系统的级联倍周期1,2, 4, 8-周期轨,在Neimark-Sacker分岔中出现了不变闭曲线、周期窗口、准周期轨道和混沌集).最后我们利用反馈控制方法把混沌轨道控制到不稳定的不动点上.随后,我们将上面模型中的双线性传染率βxy改为标准传染率βxy/x+y来进行研究,介绍了改进后的离散寄生虫-宿主模型发生Flip分岔和Neimark-Sacker分岔的动力学行为并讨论了两种模型的生物学意义.
[Abstract]:This paper mainly studies the dynamic characteristics of a simple discrete parasite-host model, which is divided into three chapters: the first chapter introduces the significance, research background and research status of this paper. In the second chapter, we introduce the relevant preparatory knowledge about the dynamic properties of the model, namely the bifurcation theory related to the model, the central manifold theorem and chaos in the sense of Marotto, and introduce the main work of this paper. In chapter 3, the Euler method is used to discretize the continuous parasite-host model, and the dynamic properties of the discrete model are studied. Firstly, the existence and stability of fixed points are discussed. By using the center manifold theorem and bifurcation theory, the conditions for the occurrence of Flip bifurcation and Neimark-Sacker bifurcation of the system are obtained. Secondly, according to the definition of Marotto chaos, the existence of chaos in the sense of Marotto is proved. The theoretical results are verified by numerical simulation, and it is found that the system has rich and complex dynamic behaviors (the cascade cycles of the system are 1, 2, 4, 8-period orbit), and the invariant closed curve and periodic window appear in the Neimark-Sacker bifurcation. Quasi-periodic orbits and chaotic sets). Finally, we use the feedback control method to control the chaotic orbit to the unstable fixed point. Then, we change the bilinear infection rate 尾 xy in the above model to the standard infection rate 尾 xy/x y. The dynamic behavior of Flip bifurcation and Neimark-Sacker bifurcation in the improved discrete parasite-host model is introduced and the biological significance of the two models is discussed.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
[Abstract]:This paper mainly studies the dynamic characteristics of a simple discrete parasite-host model, which is divided into three chapters: the first chapter introduces the significance, research background and research status of this paper. In the second chapter, we introduce the relevant preparatory knowledge about the dynamic properties of the model, namely the bifurcation theory related to the model, the central manifold theorem and chaos in the sense of Marotto, and introduce the main work of this paper. In chapter 3, the Euler method is used to discretize the continuous parasite-host model, and the dynamic properties of the discrete model are studied. Firstly, the existence and stability of fixed points are discussed. By using the center manifold theorem and bifurcation theory, the conditions for the occurrence of Flip bifurcation and Neimark-Sacker bifurcation of the system are obtained. Secondly, according to the definition of Marotto chaos, the existence of chaos in the sense of Marotto is proved. The theoretical results are verified by numerical simulation, and it is found that the system has rich and complex dynamic behaviors (the cascade cycles of the system are 1, 2, 4, 8-period orbit), and the invariant closed curve and periodic window appear in the Neimark-Sacker bifurcation. Quasi-periodic orbits and chaotic sets). Finally, we use the feedback control method to control the chaotic orbit to the unstable fixed point. Then, we change the bilinear infection rate 尾 xy in the above model to the standard infection rate 尾 xy/x y. The dynamic behavior of Flip bifurcation and Neimark-Sacker bifurcation in the improved discrete parasite-host model is introduced and the biological significance of the two models is discussed.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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