一类具有庇护效应的食饵-捕食收获模型  

A Harvesting Prey-Predator Model with Shelter Effect

作　　者：童姗姗[1] 牛玉俊[1] 窦霁虹[2] 

机构地区：[1]南阳理工学院数学与统计学院,河南南阳473004 [2]西北大学数学系,西安710127

出　　处：《河南科学》2016年第5期641-647,共7页Henan Science

基　　金：国家自然科学基金资助项目(U1504105);南阳市软科学研究计划项目(RKX06)

摘　　要：研究了一类具有庇护效应的食饵-捕食收获模型.讨论了系统平衡点的局部和全局稳定性,利用庞卡莱-班狄克逊环域定理分析了正平衡点处极限环的存在唯一性,通过Pontyagin最大值原理得到了两种群的最优收获策略.最终得到了庇护和收获效应对此系统持久性的影响,为生物资源的合理利用提供了一定实用价值.A harvesting prey-predator model with shelter effect was studied. The local and global stability of equilibriumpoints of the system was analyzed,the existence and uniqueness of limit cycle was analyzed by using the Pioncare-Bendixson ring region theorem,and the optimal harvesting policy of two populations was obtained by Pontyaginmaximum principle. Finally,the influence of shelter and harvest effect on the permanence of the system was obtained,which provided some practical value for the rational utilization of biological resources.

关 键 词：庇护效应 平衡点 极限环 最优收获 

分 类 号：O175.1[理学—数学]