一类具有食饵避难的Leslie-Gower捕食-食饵模型的定性分析

Qualitative Analysis of a Leslie-Gower Predator-prey Model Incorporating a Prey Refuge

研究了一类具有食饵避难的Leslie-Gower捕食-食饵模型.利用线性稳定性理论,得到了平衡态方程正常数解的渐进稳定性;借助分支理论,得到了以扩散系数d_2为分支参数,平衡态方程在正常数解E*处的局部分支,证明了在一定条件下,(d_2~j,E*)处产生的局部分支可以延拓成全局分支.

In this paper,we investigate the qualitative analysis of a predator-prey model,which is based on a modified version of the Leslie-Gower scheme incorporating a prey refuge.With the help of the linearized stability theory,we investigate the stability of positive constant steady state of the model.By bifurcation theory,the local bifurcation of steady-state system at the positive constant solution E*is obtained by treating as bifurcation parameter,and it is shown that under certain conditions,the local bifurcation generated can be extended to global bifurcation.