離散寄生蟲—宿主模型的動力學分析
發(fā)布時間：2019-05-03 19:51
【摘要】：本文主要研究了一類簡單的離散寄生蟲-宿主模型的動力學特性,分為如下三個章節(jié)進行討論:第一章首先介紹了本文的選題意義、研究背景及研究現(xiàn)狀.第二章介紹了研究模型動力學性質的相關預備知識即與模型有關的分岔理論、中心流形定理和Marotto意義下的混沌,并介紹了論文的主要工作.第三章用Euler方法將連續(xù)的寄生蟲-宿主模型離散化,研究離散模型的動力學性質.首先,討論了不動點的存在性和穩(wěn)定性,應用中心流形定理和分岔理論得到了系統(tǒng)發(fā)生Flip分岔和Neimark-Sacker分岔的條件.其次,根據Marotto混沌的定義證明了存在Marotto意義下的混沌.數值模擬驗證了理論結果,并發(fā)現(xiàn)此系統(tǒng)具有豐富復雜的動力學行為(系統(tǒng)的級聯(lián)倍周期1,2, 4, 8-周期軌,在Neimark-Sacker分岔中出現(xiàn)了不變閉曲線、周期窗口、準周期軌道和混沌集).最后我們利用反饋控制方法把混沌軌道控制到不穩(wěn)定的不動點上.隨后,我們將上面模型中的雙線性傳染率βxy改為標準傳染率βxy/x+y來進行研究,介紹了改進后的離散寄生蟲-宿主模型發(fā)生Flip分岔和Neimark-Sacker分岔的動力學行為并討論了兩種模型的生物學意義.
[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.
【學位授予單位】：鄭州大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：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.
【學位授予單位】：鄭州大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175
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