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一类具有Beddington-DeAngelis功能反应捕食系统收获模型的稳定性
引用本文:韩二东,郑唯唯,罗立贵.一类具有Beddington-DeAngelis功能反应捕食系统收获模型的稳定性[J].纺织高校基础科学学报,2012,25(2):145-148.
作者姓名:韩二东  郑唯唯  罗立贵
作者单位:西安工程大学理学院,陕西 西安,710048
基金项目:陕西省教育厅自然科学基金资助项目
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.

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

Stability of a predator-prey system with Beddington-DeAngelis functional response and harvesting rates
HAN Er-dong , ZHENG Wei-wei , LUO Li-gui.Stability of a predator-prey system with Beddington-DeAngelis functional response and harvesting rates[J].Basic Sciences Journal of Textile Universities,2012,25(2):145-148.
Authors:HAN Er-dong  ZHENG Wei-wei  LUO Li-gui
Affiliation:(School of Science, Xi'an Polytechnic University, Xi'an 710048, China)
Abstract: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.
Keywords:Beddington-DeAngelis functional response  asymptotic stability  Pontryagin' s maximum principle  optimal harvesting
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