具有Prey-Taxis的Holling-Tanner捕食模型的分支结构  

BIFURCATION STRUCTURES FOR A HOLLING-TANNER PREDATOR-PREY MODEL WITH PREY-TAXIS

作　　者：张晓杰 张丽娜 ZHANG Xiaojie;ZHANG Lina(College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070 ,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《数学杂志》2018年第1期140-146,共7页Journal of Mathematics

基　　金：国家自然科学基金(11061031)

摘　　要：本文研究了一类具有prey-taxis的Holling-Tanner捕食模型中的斑图生成问题.运用线性化分析的方法和经典的分支理论,证明了只有当趋化排斥发生时,由正平衡点处才可以分支出非常数正平衡解.进一步在分支点附近确定了分支方向.In this paper,we study pattern formations in a Holling-Tanner predator-prey model with prey-taxis.By using the linear analysis method and the classical bifurcation theory,it is proved that the branches of nonconstant solutions can bifurcate from the positive equilibrium only when the retreating behavior of predators occurs.Furthermore,the directions of the branches near the bifurcation points are obtained.

关 键 词：Holling-Tanner捕食模型 prey-taxis 分支 非常数正平衡解 

分 类 号：O175.26[理学—数学]