發(fā)布時(shí)間：2018-06-06 07:28

  本文選題：時(shí)滯 + Allee效應(yīng)��； 參考：《河南師范大學(xué)》2017年碩士論文

【摘要】：本文主要分析了兩類(lèi)捕食被捕食系統(tǒng)的分支問(wèn)題:一類(lèi)是帶有雙Allee效應(yīng)的單時(shí)滯捕食被捕食系統(tǒng);另一類(lèi)是含有兩個(gè)時(shí)滯的改進(jìn)的Leslie-Gower型捕食被捕食系統(tǒng).本文主要通過(guò)推廣應(yīng)用時(shí)滯微分方程的標(biāo)準(zhǔn)型理論和中心流形定理,得到對(duì)應(yīng)系統(tǒng)的開(kāi)拆標(biāo)準(zhǔn)型,進(jìn)而得到一系列有趣的分支現(xiàn)象.第一章,介紹了本文的研究背景及發(fā)展現(xiàn)狀,列出一些所需的理論知識(shí).第二章,考慮被捕食者帶有雙Allee效應(yīng)的單時(shí)滯捕食被捕食模型的分支問(wèn)題.首先給出模型在其正平衡點(diǎn)處為Bogdanov-Takens(B-T)或triple-zero型奇點(diǎn)的充分條件.然后選擇合適的分支參數(shù),通過(guò)推廣使用中心流形定理和開(kāi)拆標(biāo)準(zhǔn)型方法,分別推導(dǎo)出系統(tǒng)在B-T型奇點(diǎn)和triple-zero型奇點(diǎn)處的開(kāi)拆標(biāo)準(zhǔn)型及相應(yīng)的分支結(jié)果.第三章,主要研究具有兩個(gè)時(shí)滯改進(jìn)的Leslie-Gower型的捕食被捕食模型在其正平衡點(diǎn)處的余維分支問(wèn)題.通過(guò)分析相應(yīng)奇點(diǎn)處的特征方程的根的分布,得到奇點(diǎn)為B-T型或triple-zero型奇點(diǎn)的存在條件.通過(guò)應(yīng)用微分方程的定性理論和中心流形定理,可以得到系統(tǒng)在平衡點(diǎn)處的分支情況.
[Abstract]:In this paper, the bifurcation problems of two kinds of predator-prey systems are analyzed: one is a single-delay predator-prey system with double Allee effect, the other is an improved Leslie-Gower predator-prey system with two delays. In this paper, we generalize the canonical form theory of delay differential equation and the central manifold theorem, and obtain the open and disassembly canonical form of the corresponding system, and then obtain a series of interesting bifurcation phenomena. The first chapter introduces the research background and present situation of this paper, and lists some necessary theoretical knowledge. In chapter 2, the bifurcation problem of predator-prey model with double Allee effect is considered. The sufficient conditions for the model to be Bogdanov-Takenson B-T or triple-zero singularity at its positive equilibrium point are given. Then the proper bifurcation parameters are selected, and by using the center manifold theorem and the open and disassembly canonical form method, the open and disassembly canonical forms of the system at B-T singularities and triple-zero singularities and the corresponding bifurcation results are derived respectively. In chapter 3, we study the codimensional bifurcation of a predator-prey model with two delays at the positive equilibrium point of the predator-prey model. By analyzing the root distribution of the characteristic equations at the corresponding singularities, the existence conditions of the singularities of B-T type or triple-zero type are obtained. By applying the qualitative theory of differential equations and the central manifold theorem, the bifurcation of the system at the equilibrium point can be obtained.
【學(xué)位授予單位】：河南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 喬志琴;劉興波;朱德明;;具有三重零奇異的時(shí)滯微分方程的分支[J];數(shù)學(xué)年刊A輯(中文版);2010年01期

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本文編號(hào)：1985761