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一个具有时滞和功能反应的非自治阶段结构的捕食模型
引用本文:雒志江,高巧琴.一个具有时滞和功能反应的非自治阶段结构的捕食模型[J].数学的实践与认识,2008,38(13).
作者姓名:雒志江  高巧琴
作者单位:山西省吕梁高等专科学校,数学系,山西,离石,033000
摘    要:研究一个具有时滞和功能反应的非自治阶段结构的捕食模型,其中食饵种群分两个阶段——幼年和成年,且捕食种群只捕成年食饵.通过利用微分不等式、比较定理和构造适当的Lyapunov泛函,得到该模型的永久持续生存和绝灭的充分条件,同时也得到了周期系统存在唯一全局渐近稳定的周期解的充分条件.

关 键 词:阶段结构  时滞  功能反应  永久持续生存和绝灭  周期解

A Non-autonomous Stage-Structure Predator-Prey System with Delay and Functional Response
LUO Zhi-jiang,GAO Qiao-qin.A Non-autonomous Stage-Structure Predator-Prey System with Delay and Functional Response[J].Mathematics in Practice and Theory,2008,38(13).
Authors:LUO Zhi-jiang  GAO Qiao-qin
Abstract:A predator-prey model with delay and functional response and stage structure for prey is studied.By using differential inequality and comparison theorem,it is obtained that the system is permanence and extinction under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is global asymptotic stable under appropriate conditions by constructed suitable lyapunov functional.
Keywords:stage-structure  delay  functional response  permanence and extinction  periodic solution
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