本文關(guān)鍵詞：捕食與食餌問題的動(dòng)力學(xué)分析　出處：《天津工業(yè)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Allee效應(yīng) Lyapunov函數(shù) 持久穩(wěn)定 動(dòng)力學(xué)行為 隨機(jī)有界性 隨機(jī)持久性 全局吸引性 滅絕

【摘要】：種群生態(tài)學(xué)是描述生物種群和環(huán)境之間的相互作用關(guān)系的一門學(xué)科.許多生物學(xué)家和數(shù)學(xué)家將這種復(fù)雜的相互作用關(guān)系建立成數(shù)學(xué)模型表示,以便用來描述以及預(yù)測(cè)生物種群的發(fā)展過程,進(jìn)而通過人為的作用進(jìn)一步調(diào)節(jié)和控制種群的生存發(fā)展,以便達(dá)到使得種群持久穩(wěn)定的狀態(tài)。本文主要對(duì)幾類非線性種群系統(tǒng)的動(dòng)力學(xué)行為進(jìn)行了深入的分析與研究.主要考慮了 Allee效應(yīng)、捕獲、隨機(jī)噪聲等因素對(duì)生物系統(tǒng)的穩(wěn)定性所產(chǎn)生的影響,主要通過構(gòu)造Lyapunov函數(shù)及利用隨機(jī)過程理論等方法研究了種群系統(tǒng)的動(dòng)力學(xué)行為.本文的主要內(nèi)容如下:1.研究了一類具有Allee效應(yīng)的兩種群捕食模型,并對(duì)該系統(tǒng)的捕食者與食餌施加捕獲,通過對(duì)模型進(jìn)行定性分析,證明了正平衡點(diǎn)的存在性和穩(wěn)定性,進(jìn)一步通過數(shù)值模擬加以驗(yàn)證.結(jié)果表明對(duì)系統(tǒng)應(yīng)合理進(jìn)行捕獲,這樣才能使種群持久穩(wěn)定.2.研究了一類具有HollingⅡ功能反應(yīng)的兩種捕食者與一種食餌之間關(guān)系的捕食模型,通過分析特征方程,Routh-Hurwitz準(zhǔn)則及計(jì)算Lyapunov指數(shù),分析了確定性系統(tǒng)平衡點(diǎn)的穩(wěn)定性,進(jìn)一步借助數(shù)值模擬分析了系統(tǒng)的穩(wěn)定性.3.建立并研究了一類具有HollingⅡ功能反應(yīng)函數(shù)互惠隨機(jī)模型.得出,對(duì)于任意給定的初值該模型有全局唯一正解以及此解具有隨機(jī)有界性.另外,經(jīng)過定性分析,給出了系統(tǒng)唯一正解的隨機(jī)持久性和全局吸引性的存在條件.同時(shí)發(fā)現(xiàn)當(dāng)環(huán)境噪聲較小時(shí),隨機(jī)模型與確定性模型的種群衍化情形類似,否則種群將最終滅亡.由此可知考慮環(huán)境的隨機(jī)性是非常必要的.文中每一部分都通過數(shù)值模擬證明了結(jié)論的正確性.
[Abstract]:Population ecology is a discipline to describe the relationship between population and environment. The interaction between many biologists and mathematicians will establish a mathematical model of this complex that can be used to describe and predict the development of biological population, and then through the people for the role to further regulate and control the survival and development of the population, in order to achieve the permanence stable state. The main dynamical behavior of several nonlinear population system in-depth analysis and research. The main consideration of the Allee effect, capture effect of random noise impact on the stability of biological system, mainly through the construction of Lyapunov function and using the stochastic process theory and method to study the dynamic behavior population system. The main contents of this paper are as follows: 1. of the two species predator-prey model with Allee type effect And, the predator and prey capture is applied in the system, through the qualitative analysis of the model, we prove the existence and stability of positive equilibrium, further verified through numerical simulation. The results show that the system should be reasonable to capture, so as to make the population lasting stable predator-prey model is studied for a class of.2. with Holling II the functional response of two species of predators and one prey relationship, through the analysis of the characteristic equation, Routh-Hurwitz criterion and Lyapunov index calculation, the stability of the equilibrium point of the system uncertainty analysis, further by means of numerical simulation analysis of the stability of.3. system is established and studied a class of Holling functional response function. The reciprocal stochastic model with. For any given initial value of the model has a unique positive solution and the global solution with stochastic boundedness. In addition, through qualitative analysis, gives the system is only The existence conditions of attractive solutions for stochastic permanence and global environment. At the same time that when the noise is small, stochastic models and deterministic models of population derived from a similar situation, otherwise the population will eventually perish. Thus considering random environment is very necessary. In this paper, each part through numerical simulation validates the conclusion.

【學(xué)位授予單位】：天津工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前7條

1 王萬雄;趙燦省;張艷波;;一類具有Allee效應(yīng)的捕食系統(tǒng)的穩(wěn)定性分析及模擬[J];數(shù)學(xué)的實(shí)踐與認(rèn)識(shí);2013年20期

2 黃運(yùn)金;張朝陽;;無窮時(shí)滯Lotka-Volterra競(jìng)爭(zhēng)系統(tǒng)的持久性[J];福建農(nóng)林大學(xué)學(xué)報(bào)(自然科學(xué)版);2010年02期

3 周少波;胡適耕;;RAZUMIKHIN-TYPE THEOREMS OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS[J];Acta Mathematica Scientia;2009年01期

4 王洪禮,馮劍豐,沈菲,孫景;赤潮藻類非線性動(dòng)力學(xué)模型的分岔及穩(wěn)定性研究[J];應(yīng)用數(shù)學(xué)和力學(xué);2005年06期

5 岳宗敏,胡志興;一類具功能反應(yīng)的食餌-捕食者兩種群模型的極限環(huán)的唯一性[J];生物數(shù)學(xué)學(xué)報(bào);2005年02期

6 鄭靖波,余昭旭,孫繼濤;一類稀疏效應(yīng)下食餌-捕食系統(tǒng)極限環(huán)的存在唯一性[J];生物數(shù)學(xué)學(xué)報(bào);2001年02期

7 梁肇軍;陳蘭蓀;;食餌種群具有常數(shù)收獲率的二維VOLTERRA模型的定性分析[J];生物數(shù)學(xué)學(xué)報(bào);1986年01期

，

本文編號(hào)：1357064