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

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