【摘要】：在現(xiàn)實(shí)世界中種群的生存發(fā)展會受環(huán)境噪聲、時滯、脈沖和捕獲等多種因素的共同作用.因此在建立種群的生態(tài)模型時這些因素的考慮是很有必要的.本文利用隨機(jī)微分方程,泛函分析和脈沖微分方程的相關(guān)理論知識研究了兩類非自治脈沖隨機(jī)時滯單種群模型的持久生存性和絕滅性,并給出了具體的數(shù)值例子.全文共分為四章:第一章概述了本文所研究內(nèi)容的研究背景、研究意義和國內(nèi)外研究現(xiàn)狀,也簡單介紹了本文的主要工作.第二章給出了與本文相關(guān)的一些記號,引入了相關(guān)的定義、引理和一些不等式.第三章提出并研究了兩類具有捕獲項(xiàng)的非自治脈沖隨機(jī)時滯單種群模型,得到了隨機(jī)持久性的充分條件.最后用幾個具體的數(shù)值例子驗(yàn)證了理論結(jié)果的可行性.第四章提出并研究了兩類具有Lévy噪聲和捕獲項(xiàng)的非自治脈沖隨機(jī)時滯單種群模型,得到了絕滅性,非平均持久性,弱持久性和隨機(jī)持久性的充分條件.最后用幾個具體的數(shù)值例子驗(yàn)證了理論結(jié)果的可行性.
[Abstract]:In the real world, the survival and development of the population will be affected by environmental noise, time delay, pulse and capture and other factors. Therefore, it is necessary to consider these factors in establishing ecological model of population. In this paper, we use the theory of stochastic differential equation, functional analysis and impulsive differential equation to study the persistence and extinction of two kinds of nonautonomous impulsive stochastic delay single population models, and give some numerical examples. The paper is divided into four chapters: the first chapter summarizes the research background, research significance and domestic and foreign research status, and also briefly introduces the main work of this paper. In the second chapter, we give some notations related to this paper, and introduce some definitions, Lemma and some inequalities. In chapter 3, two kinds of nonautonomous impulsive stochastic delay single population models with capture term are proposed and studied, and the sufficient conditions for stochastic persistence are obtained. Finally, several numerical examples are given to verify the feasibility of the theoretical results. In chapter 4, two kinds of nonautonomous impulsive stochastic time-delay single population models with L 茅 vy noise and capture term are proposed and studied. Sufficient conditions for extinction, non-mean persistence, weak persistence and stochastic persistence are obtained. Finally, several numerical examples are given to verify the feasibility of the theoretical results.
【學(xué)位授予單位】：湖北民族學(xué)院
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：2168024