两类具有捕获项的非自治脉冲随机时滞单种群模型的研究
发布时间：2018-08-06 14:28
【摘要】：在现实世界中种群的生存发展会受环境噪声、时滞、脉冲和捕获等多种因素的共同作用.因此在建立种群的生态模型时这些因素的考虑是很有必要的.本文利用随机微分方程,泛函分析和脉冲微分方程的相关理论知识研究了两类非自治脉冲随机时滞单种群模型的持久生存性和绝灭性,并给出了具体的数值例子.全文共分为四章:第一章概述了本文所研究内容的研究背景、研究意义和国内外研究现状,也简单介绍了本文的主要工作.第二章给出了与本文相关的一些记号,引入了相关的定义、引理和一些不等式.第三章提出并研究了两类具有捕获项的非自治脉冲随机时滞单种群模型,得到了随机持久性的充分条件.最后用几个具体的数值例子验证了理论结果的可行性.第四章提出并研究了两类具有Lévy噪声和捕获项的非自治脉冲随机时滞单种群模型,得到了绝灭性,非平均持久性,弱持久性和随机持久性的充分条件.最后用几个具体的数值例子验证了理论结果的可行性.
[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.
【学位授予单位】：湖北民族学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2168024
[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.
【学位授予单位】：湖北民族学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前2条
1 卢春;丁效华;;PERSISTENCE AND EXTINCTION OF A STOCHASTIC LOGISTIC MODEL WITH DELAYS AND IMPULSIVE PERTURBATION[J];Acta Mathematica Scientia;2014年05期
2 ;Existence,uniqueness,and global attractivity of positive solutions and MLE of the parameters to the Logistic equation with random perturbation[J];Science in China(Series A:Mathematics);2007年07期
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