【摘要】：捕食者-食餌系統(tǒng)是一類經(jīng)典的生物模型,它刻畫了不同種群間的一種相互作用關(guān)系.對該系統(tǒng)行波解和漸近傳播速度的深入研究,可以解釋和預(yù)測自然界中的某些生物現(xiàn)象,因此它在過去的幾十年里被廣泛地關(guān)注.但這其中大多數(shù)的結(jié)果只考慮了帶有常系數(shù)的反應(yīng)擴(kuò)散系統(tǒng)的行波解以及漸近傳播,而具有時間周期的系統(tǒng)的相關(guān)結(jié)果卻很少.因此,本文將主要研究帶有時間周期的Lotka-Volterra捕食者-食餌反應(yīng)擴(kuò)散系統(tǒng)的行波解和漸近傳播速度.本文首先研究了該系統(tǒng)的周期行波解的存在性和漸近行為.先構(gòu)造一組合適的上下解從而得到一個由周期函數(shù)構(gòu)成的非空閉凸集,然后在此集上定義非線性算子,再利用Schauder不動點(diǎn)定理得到非平凡周期行波解的存在性.還結(jié)合漸近傳播理論和全局漸近穩(wěn)定周期解的一些收斂結(jié)果,給出了行波解的漸近行為.此外,根據(jù)比較原理和漸近傳播理論,建立了行波解的不存在性.最后在兩種不同的假設(shè)條件下討論了該系統(tǒng)的漸近傳播速度,其基本方法是利用漸近傳播理論,并結(jié)合輔助方程和比較原理.情形一,捕食者在共同入侵棲息地過程中占優(yōu)勢時,本文得到了捕食者的傳播速度和食餌傳播速度的上下界.結(jié)果表明捕食者的傳播速度可以不受種群間相互作用的影響,而食餌的傳播速度會減慢,也就是捕食者對食餌的種群的發(fā)展起負(fù)作用.情形二,當(dāng)食餌入侵占優(yōu)勢時,文中得到了食餌的傳播速度和捕食者傳播速度的一個下界.結(jié)果表明種群間的相互作用可以不改變食餌的傳播速度,卻會加快捕食者的傳播速度,即食餌能促進(jìn)捕食者種群的發(fā)展.
[Abstract]:Predator-prey system is a classical biological model, which describes the interaction between different populations. The study of traveling wave solution and asymptotic propagation velocity of this system can explain and predict some biological phenomena in nature, so it has been paid more and more attention in the past few decades. However, most of the results only consider the traveling wave solution and asymptotic propagation of the reaction diffusion system with constant coefficients, but the correlation results of the system with time period are few. Therefore, the traveling wave solution and asymptotic propagation velocity of Lotka-Volterra predator-prey reaction diffusion system with time period will be studied in this paper. In this paper, the existence and asymptotic behavior of periodic traveling wave solutions for the system are studied. A set of suitable upper and lower solutions is constructed to obtain a nonempty closed convex set composed of periodic functions. Then nonlinear operators are defined on the set, and then the existence of nontrivial periodic traveling wave solutions is obtained by using Schauder fixed point theorem. The asymptotic behavior of traveling wave solutions is also given by combining the asymptotic propagation theory and some convergence results of globally asymptotically stable periodic solutions. In addition, according to the comparison principle and asymptotic propagation theory, the nonexistence of traveling wave solution is established. Finally, the asymptotic propagation velocity of the system is discussed under two different assumptions. The basic method is to use the asymptotic propagation theory, combined with the auxiliary equation and the principle of comparison. In the first case, when the predator is dominant in the process of invading the habitat together, the upper and lower bounds of the predator's propagation speed and the prey's propagation speed are obtained in this paper. The results show that the propagating speed of predator can not be affected by the interaction between populations, but the propagation speed of prey will slow down, that is, the predator plays a negative role in the development of prey population. In the second case, when the prey invasion is dominant, a lower bound of the propagation speed of prey and predator is obtained. The results show that the interaction between populations can not change the propagation speed of prey, but accelerate the spread of predator, that is, prey can promote the development of predator population.
【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 薄偉健;周期弱競爭Lotka-Volterra系統(tǒng)的行波解和漸近傳播[D];蘭州大學(xué);2016年

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本文編號：2406282