一个基于比率确定的捕食与被捕食收获模型的定性分析  

Qualitative analysis of a ratio-dependent predator-prey system with harvesting rate

作　　者：李晶晶[1] 水树良[1] 张旭杨[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2010年第4期411-416,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(10771196);浙江省自然科学基金资助项目(Y7080198)

摘　　要：研究了一类具有HollingⅡ功能反应且比率确定的捕食与被捕食模型在非线性状态反馈收获下所表现的动力学性态.在给定的生物参数与控制参数满足一定条件的情形下,讨论了该模型正平衡点的存在性与稳定性,分析了产生分支的条件,并证明了极限环的存在性与不存在性.A ratio-dependent predator-prey system with harvesting rate was studied.Under some conditions for the biological or controlling parameter,the existence and stability for the positive equilibrium points were discussed,and the bifurcation values of the equilibrium points were obtained.Conditions for the existence and nonexistence of limit cycles around the positive equilibrium points were also obtained.

关 键 词：捕食模型 平衡点 分支 极限环 

分 类 号：O175[理学—数学]