斑块环境下两类具有Beddington-DeAngelis功能反应函数和时滞的捕食者—食饵模型
发布时间：2018-11-04 21:20
【摘要】：本论文主要研究了斑块环境下两类具有Beddington-DeAngelis功能反应函数和时滞的捕食者-食饵模型.首先,介绍了有关的背景知识和一些预备知识.其次,考虑了斑块环境下具有单一捕食者的捕食者-食饵模型,通过构造(1-函数的方法,借助已知的辅助系统,利用比较定理,给出了具有单一捕食者的捕食者-食饵模型持久性和灭绝性的充分条件.接着考虑了斑块环境下具有两种捕食者的捕食者-食饵模型,考虑捕食者之间的竞争关系,借助已知的辅助系统,利用比较定理,给出了该捕食者-食饵系统的持久性的充分条件.并且借助庞加莱映射考虑了该捕食者-食饵模型的周期解的存在性.最后通过构建适当的Lyapunov函数的方法得到了该系统存在唯一的全局渐近稳定的正解.
[Abstract]:In this paper, two kinds of predator-prey models with Beddington-DeAngelis functional response function and time-delay in patch environment are studied. First, the background knowledge and some preparatory knowledge are introduced. Secondly, the predator-prey model with a single predator in patch environment is considered. By constructing (1-function), by means of the known auxiliary system, the comparison theorem is used. Sufficient conditions for permanence and extinction of predator-prey models with a single predator are given. Then considering the predator-prey model with two kinds of predators in patch environment, considering the competition between predators, and using the known auxiliary system, the comparison theorem is used. A sufficient condition for the permanence of the predator-prey system is given. The existence of periodic solutions of the predator-prey model is considered by means of the Poincare mapping. Finally, by constructing the appropriate Lyapunov function, we obtain the unique positive solution of the system with globally asymptotically stable.
【学位授予单位】：烟台大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2311169
[Abstract]:In this paper, two kinds of predator-prey models with Beddington-DeAngelis functional response function and time-delay in patch environment are studied. First, the background knowledge and some preparatory knowledge are introduced. Secondly, the predator-prey model with a single predator in patch environment is considered. By constructing (1-function), by means of the known auxiliary system, the comparison theorem is used. Sufficient conditions for permanence and extinction of predator-prey models with a single predator are given. Then considering the predator-prey model with two kinds of predators in patch environment, considering the competition between predators, and using the known auxiliary system, the comparison theorem is used. A sufficient condition for the permanence of the predator-prey system is given. The existence of periodic solutions of the predator-prey model is considered by means of the Poincare mapping. Finally, by constructing the appropriate Lyapunov function, we obtain the unique positive solution of the system with globally asymptotically stable.
【学位授予单位】：烟台大学
【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 李海银;;具有密度制约和Beddington-DeAngelis功能反应函数的周期捕食-被捕食系统的持久性[J];应用数学学报;2014年05期
2 董士杰,葛渭高;具有时滞和基于比率的两种群捕食者-食饵扩散系统的周期解[J];应用数学学报;2004年01期
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