文献类型：期刊文献

中文题名：带有阶段结构的时滞捕食-被捕食动力系统的全局稳定性和最优收获量(英文)

英文题名：Stability and Optimal Harvesting of a Delayed Ratio-Dependent Predator-Prey System with Stage Structure

作者：李海银[1];张瑞[1]

机构：[1]河南财经学院信息学院

第一机构：河南财经政法大学计算机与信息工程学院

年份：2008

卷号：23

期号：1

起止页码：40-52

中文期刊名：生物数学学报

外文期刊名：Journal of Biomathematics

收录：北大核心:【北大核心2004】；CSCD:【CSCD2011_2012】；

语种：中文

中文关键词：阶段结构;最优收获量;基于比率;时滞;全局稳定性

外文关键词：Stage structure ; Optimal harvesting ; Ratio-dependent ; Time delay ; Global asymptotic stability

摘要：讨论捕食和被捕食动力系统时,把生物种群分为幼年和成年两个阶段,仅成年有捕食能力.还考虑了种群相互作用中不可避免的时滞和密度制约作用,以及在捕食一被捕食模型中更切合实际的"比率依赖"理论.通过对系统的分析和构造李雅普诺夫函数,分别得出在适当条件下系统非负平衡位置的局部稳定性和全局稳定性,并研究了成熟种群的最优收获量.
A stage-structured predator-prey system of population growth con-sisting of immature and mature individuals is proposed with a mature population of harvesting, the growth of predator population is of Holling II type with time delay and ratio-dependent（which can be roughly stated as that the per capita predator growth rate should be a function of the ratio of prey to predator abundance）. We establish conditions under which positive equilibrium of the system is locally and globally asymp- totically stable and the optimal harvesting of the mature population is also considered.