一类带Michaelis-Menten收获项的Holling-Ⅳ型捕食-食饵模型的定性分析  

The Qualitative Analysis of a Holling-Ⅳ Type Predator-prey Model with Michaelis-Menten Type Prey Harvesting

作　　者：周翔宇[1] 吴建华[1] Zhou Xiangyu;Wu Jianhua(College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China)

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《应用数学学报》2019年第1期32-42,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11271236)资助项目

摘　　要：本文对一类带Michaelis-Menten收获项的Holling-Ⅳ型捕食-食饵模型进行了定性分析.首先,利用极值原理和线性稳定性理论,得到了平衡态方程解的先验估计和正常数解的局部渐近稳定性;然后,借助分歧理论,给出了以d2为分歧参数,平衡态方程在正常数解U_1处的局部分歧,证明了在一定条件下,(d_2~j,U_1)处产生的局部分歧可以延拓成全局分歧.In this paper, a Holling-IV type predator-prey model with Michaelis-Menten type harvesting is qualitatively analyzed. At first, by the maximum principle and the linearized stability theory, a priori estimates of the steady-state system and the local asymptotic stability of positive constant solutions are given. Then, with the help of bifurcation theory,the local bifurcation of steady-state system at the positive constant solution U1 is obtained by treating d2 as bifurcation parameter;it is shown that under certain conditions, the local bifurcation generated from(d2j,U1) can be extended to global bifurcation.

关 键 词：捕食-食饵模型 Holling-Ⅳ型 渐近稳定性 分歧理论 

分 类 号：O175.26[理学—数学]