具收获率的Holling-Ⅳ型两种群生物系统的定性分析  

A Qualitative Analysis of Two Groups of Holling-Ⅳ Biological Systems with Harvest Rate

作　　者：李冰森 赵育林[1] 张子龙 LI Bingsen;ZHAO Yulin;ZHANG Zilong(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China;School of Mathematics and Statistics,Central South University,Changsha 410083,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007 [2]中南大学数学与统计学院,湖南长沙410083

出　　处：《湖南工业大学学报》2020年第1期1-8,F0002,共9页Journal of Hunan University of Technology

基　　金：湖南省自然科学基金资助项目(2019JJ40068)

摘　　要：对一类具有收获率的Holling-Ⅳ型食饵-捕食者系统作定性分析,利用Poincare形式级数法、Poincare-Bendixson环域定理、Dulac定理及分支理论等,得到了此系统平衡点的性态、正平衡点的焦点量、极限环存在和不存在性的条件,并借助数学软件对主要结果进行了数值验证。A qualitative analysis has been made of a class of Holling-Ⅳprey-predator systems with the harvest rate.By using Poincare formal series method,Poincare Bendixson ring domain theorem,Dulac theorem and branch theory,such statistics as the behavior of equilibrium point,the focus quantity of positive equilibrium point,the existence and nonexistence conditions of limit cycle can be obtained,with the main results to be verified via mathematical software.

关 键 词：收获率 Holling-Ⅳ型 极限环 食饵-捕食系统 

分 类 号：O175[理学—数学]