一类具有Beddington-DeAngelis功能反应捕食系统收获模型的稳定性  

Stability of a predator-prey system with Beddington-DeAngelis functional response and harvesting rates

作　　者：韩二东[1] 郑唯唯[1] 罗立贵[1] 

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2012年第2期145-148,共4页Basic Sciences Journal of Textile Universities

基　　金：陕西省教育厅自然科学基金资助项目(11JK0502)

摘　　要：研究一类具有双线性密度制约及Beddington-DeAngelis功能反应的捕食系统收获模型.运用微分方程定性稳定性理论讨论系统正平衡点的性态,得到其局部渐近稳定及全局渐近稳定的充分条件,利用Pontryagin最大值原理得到系统的最优收获策略.A predator-prey system with Beddington-DeAngelis functional response and selective harves- ting rates of predator species is given,where prey and predator both has linear density dependent. Using ordinary differential equations characterization and stability,the existence and uniqueness of positive e- quilibriums was studied. The sufficient conditions of its global asymptotic stability and local asymptotic stability are given. An optimal taxation policy is obtained by Pontryagin＇s maximum principle.

关 键 词：Beddington-DeAngelis功能反应 渐近稳定 Pontryagin最大值原理 最优收获策略 

分 类 号：O175.13[理学—数学]