具有HollingⅡ型功能反应的捕-食模型的定性分析及最优收获策略  

Qualitative Analysis and Optimal Harvesting Strategy of Predator-prey Model with HollingII Functional Response

作　　者：冯光庭[1] 赵换 张兴安[3] 

机构地区：[1]湖北第二师范学院数学与数量经济学院,湖北武汉430205 [2]福建省厦门市第九中学,福建厦门361004 [3]华中师范大学数学与统计学学院,湖北武汉430079

出　　处：《数学的实践与认识》2013年第12期191-197,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11071275);湖北省教育厅科学技术重点项目(D20113005)

摘　　要：利用微分方程的定性理论和Pontryagin最大值原理,讨论了一类食饵-捕食者种群都具有密度制约并且都具有收获的HollingⅡ型功能反应模型的性质,得到了存在边界平衡点、唯一正平衡点及各平衡点全局渐进稳定的条件,分析了相应的生物学意义,给出了最优可持续收获策略,并且用mathematica对特定参数下的系统进行了模拟.By using qualitative analysis theory of differential equation and the Pontrjagin maximum value principle, a kind of predator-prey model with HollingII functional response is investigated. This model has density restriction and has harvesting. We obtained the conditions of the existence of the boundary equilibriums and the unique positive equilibrium, and we also obtained the conditions of the global asymptotic stability of these equilibriums. We analyzed the corresponding biological significance, and gave the optimal harvesting strategy. Then we carried on the simulation to the system under a group of specific parameters by using the rnathematica software.

关 键 词：HollingⅡ型功能反应 平衡点 全局渐进稳定 最优收获策略 

分 类 号：O175[理学—数学]