兰州大学机构库 >数学与统计学院
脉冲干扰下种群动力系统的研究
Alternative TitleThe Studies on Population with Impulsive Perturbation
郭中凯
Thesis Advisor李自珍
2010-05-29
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword$Floquet$ 理论 生物控制 分布时滞 脉冲干扰 比较原则 全局稳定性
Abstract近些年来生物数学中用动力系统作为工具的研究取得了长足的发展,其中以微分方程为模型的研究主要集中在连续动力系统和脉冲动力系统上。随着研究的深入,对模型的建立要求更高,希望能够真实的反映客观事实,其中连续动力系统是过去研究生物数学的主要工具,但人们发现自然界许多生命现象以及人类的一些行为如动物的季节性繁殖,人类的放养捕捞,喷洒杀虫剂以及免疫防疫相对于整个过程他们都是瞬时发生量的骤增或骤减,用连续动力系统无法精确描述,而脉冲微分方程可以相对真实的刻画这些相对短暂的现象和行为。这使得脉冲微分方程的研究和应用得到越来越多的从事生物数学研究的学者的关注。本文研究基于不同应用背景的三个生态数学模型,考察 脉冲微分系统对它们的影响。第一章简单介绍研究的背景和近年的研究展望以及脉冲微分方程的一些定义和预备知识。第二章以农业生产中的害虫防治为应用背景,我们建立和研究具有脉冲干扰的害虫传染病模型,也即是在不同时刻,周期性的喷洒微生物杀虫剂和投放被感染的害虫。 通过使用Floquet 理论和脉冲比较原则,我们证明投放被感染害虫的数量超过临界值 时害虫灭绝的周期解是全局稳定的。第三章将在对顶级捕食者进行脉冲干扰,即周期性的向食物链中投放定量的顶级捕食者的前提下,研究三种群食物链系统的稳定性。首先给出捕食者灭绝的周期解。 然后利用脉冲微分方程的比较原则和~$Floquet$ 理论,证明当脉冲周期小于某个阈值时,捕食者灭绝的周期解是全局渐近稳定的。第四章研究了脉冲干扰对具有分布时滞的三物种食物链系统。首先, 利用脉冲微分方程的~$Floquet$ 理论和比较原则得到了捕食者灭绝的周期解的全局稳定的充分条件。 同时给出了三物种持续生存的充分条件。 最后分析了顶级捕食者投放量对三物种食物链系统的影响。
Other AbstractThe need for describing more actual system impels the evolution of mathematical biological models.In recent years,the researches in mathematical biology which modeled by normal differential equations are mainly concentrated on two branches:1)continuous biological dynamical systems;2)impulsive semi-dynamical systems.The discussions of continuous biological dynamical systems were main research direction in the past decades ,people find recently that continuous biological dynamical systems can not represent some natural phenomena and control behavior of human accurately;impulsive semi-dynamical systems then turn out to be the hotspot of mathematical biology because the relatively instantaneous behavior mentioned above can be described well in impulsive differential equations.Our three models in this paper which have different applicative background is of kind of differential system.In chapter 1,We introduce concisely some definitions and fundamental theories of differential equations and impulsive differential equations.In chapter 2,Based on biological control strategy in pest management,we construct and investigate a pest-epidemic model with impulsive control,i.e.,periodic spraying microbial pesticide and releasing infected pests at different fixed moments.By using Floquet theorem and comparison theorem,we prove that the pest-eradication periodic solution is globally asymptotically stable when the impulsive releasing infective pest more than the critical value .In chapter 3,In this paper,we investigated a three trophic level food chain system with periodic constant impulsive perturbations for top predator .Firstly,predator eradications periodic solution of top predator are given.Afterward,by using comparison theorem of impulsive equation and Floquet theory ,we prove that the predator eradications periodic solution is globally asymptotically stable when impulsive period$ T$ is less than the critical value.In chapter 4,In this article ,three species food chain system with impulsive perturbations and distributed time delay is investigated.Firstly,by using Floquet theory of impulsive differential equation and comparison theorem,the global stability of predator eradication periodic solution is considered.Secondly,we obtain the conditions which guarantee the permanence of three species.Finally,we analysis the effects of impulsive release for top predator on three food chain system.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224852
Collection数学与统计学院
Recommended Citation
GB/T 7714
郭中凯. 脉冲干扰下种群动力系统的研究[D]. 兰州. 兰州大学,2010.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Altmetrics Score
Google Scholar
Similar articles in Google Scholar
[郭中凯]'s Articles
Baidu academic
Similar articles in Baidu academic
[郭中凯]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[郭中凯]'s Articles
Terms of Use
No data!
Social Bookmark/Share
No comment.
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.