几类生态模型的动力学研究

【作者】 王玲；

【导师】 张广；

【作者基本信息】 中北大学 ， 应用数学， 2011， 硕士

【摘要】 现实世界里,无论是工程中,经济方面还是生态系统中,时滞都是普遍存在的。近几十年来,时滞一直都是人们讨论的热门话题。本文在前人工作的基础上,主要研究了以下问题:第二章,讨论了一类多时滞有捕获的Leslie-Gower型捕食系统,分析了模型正平衡点的稳定性以及Hopf分支的存在性。应用规范型和中心流形理论,得到了确定了分支方向和周期解的稳定性的计算公式。第三章,研究了一类具有时滞的一食饵-两竞争捕食者模型,两捕食者竞争同一种食饵,其功能反应函数分别为Holling I型和Holling II型。选择时滞作为分支参数,发现当时滞穿过一个临界值是会发生Hopf分支。第四章,考虑了一食饵染病的食饵-捕食系统,这里的食饵是常数输入的,捕食者的功能反应是HollingII型,模型引入了疾病的潜伏期作为时滞,系统的稳定性,分支的周期解,超临界分支,亚临界分支都一一讨论。强调了潜伏期在控制生态流行病系统的重要性。以上模型都用Matlab进行了数值模拟。更多还原

【Abstract】 In the natural word, time delay is a common phenomenon in enjineering, economicaland biclogical systems,and has become a popular research topic in recent years.In this paper,according to the study of systems both at home and abroad in recent years, we carefullystudied the following three dynamic models :In chapter 2, A Leslie-Gower predator-prey system with delays and harvesting is investi-gated.We discuss the stability of a postive equilibrium and the existence of Hopf bifurcation.By using the normal form theory and center manifold reduction ,we derive explicit formuladetermining the properties of bifurcating periodic solutions.In chapter 3, we consider a delayed two-competitor,one-prey system in which the com-petitors exhibit Holling-I and Holling-II functional response.By choosing the time delay asa bifurcation parameter,it is found that the Hopf bifurcation occurs when the delay passesthrough a certain critical value .In chapter 4,this paper deals with predator-prey system where the prey population isinfected with a microparasite and with constant input ,predator functional is assumed tobe Holling-II .The model is then modi?ed to incorporate a time delay,describing a latencyperiod .Stability and bifurcation analysis of the bifurcating solutions is performed and thecriteria of subcritical and supercritical derived .The analysis emphasizes the importancelatency period in controlling disease dynamics . To above mentioned models ,we illustratedthem by Matlab.更多还原