本文選題：捕食-獵物模型 + 分歧理論�。� 參考：《華東師范大學》2017年碩士論文

【摘要】：本文主要考慮在空間非齊性環(huán)境下,研究帶有Holling-Tanner功能反應函數(shù)的捕食獵物模型的動力行為.即在平衡態(tài)下研究該模型半平凡解的穩(wěn)定性和正解的存在性.本文研究中涉及到上下解方法、極值原理、Fredholm二擇一定理、分歧理論以及不動點指標理論等.本文共有四章內(nèi)容:第一章簡單介紹捕食獵物模型的國內(nèi)外研究情況、本文所要研究的內(nèi)容以及本文的結構安排.第二章主要介紹研究本文所需要的相關概念、基本定理及結論.第三章利用特征值理論研究該模型在半平凡解處的穩(wěn)定性.第四章將從兩個方面對該模型的正解存在性展開研究,首先,獲取該模型正解的先驗估計與存在正解的必要條件,此處主要利用了極值原理和構造上下解方法兩方面的理論;然后,利用局部分歧理論推導出該模型存在正解的充分條件;最后,通過全局分歧理論與不動點指標理論對該模型進行分析,進一步將該模型在半平凡解處產(chǎn)生的局部分歧延拓到全局分歧.
[Abstract]:In this paper, the dynamic behavior of predator-prey model with Holling-Tanner functional response function is studied in a spatially inhomogeneous environment. The stability and the existence of positive solutions of the semi-trivial solutions of the model are studied in equilibrium state. In this paper, the method of upper and lower solutions, the principle of extreme value and Fredholm's alternative theorem, the theory of bifurcation and the theory of fixed point index are discussed. There are four chapters in this paper: the first chapter briefly introduces the research situation of prey model at home and abroad, the content of this paper and the structure of this paper. The second chapter mainly introduces the related concepts, basic theorems and conclusions needed to study this paper. In chapter 3, the stability of the model at the semi-trivial solution is studied by using eigenvalue theory. In chapter 4, the existence of positive solution of the model is studied from two aspects. Firstly, the priori estimate and necessary condition of the positive solution of the model are obtained. In this chapter, the theory of extreme value principle and the method of constructing upper and lower solutions are mainly used. Then, the sufficient conditions for the existence of positive solutions of the model are derived by using the local bifurcation theory. Finally, the global bifurcation theory and the fixed point index theory are used to analyze the model. Furthermore, the local bifurcation generated by the model at the semi-trivial solution is extended to the global bifurcation.
【學位授予單位】：華東師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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本文編號：1775208