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Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge. (English) Zbl 1186.34062

From the introduction: The aim of this paper is to consider instability and global stability properties of the equilibria and the existence and uniqueness of limit cycles of the following model with Holling type II functional response incorporating a constant prey refuge $m$

$\begin{array}{cc}& \stackrel{˙}{x}=\alpha x\left(1-\frac{x}{k}\right)-\frac{\beta \left(x-m\right)y}{1+a\left(x-m\right)}\phantom{\rule{0.166667em}{0ex}},\hfill \\ & \stackrel{˙}{y}=-dy+\frac{c\beta \left(x-m\right)y}{1+a\left(x-m\right)}\phantom{\rule{0.166667em}{0ex}},\hfill \end{array}\phantom{\rule{2.em}{0ex}}\left(1\right)$

where $x,y$ denote prey and predator population respectively at any time $t,d,k,\alpha ,\beta ,a,c,m$ are positive constants.

##### MSC:
 34C60 Qualitative investigation and simulation of models (ODE) 34C05 Location of integral curves, singular points, limit cycles (ODE) 34D20 Stability of ODE 92D25 Population dynamics (general)
##### References:
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