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Zbl 1186.34062
Chen, Liujuan; Chen, Fengde; Chen, Lijuan
Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 1, 246-252 (2010). ISSN 1468-1218

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 $m$ $$\aligned & \dot x=\alpha x\left(1-\frac xk\right)-\frac{\beta(x-m)y}{1+a(x-m)}\,,\\ & \dot y=-dy + \frac{c\beta(x-m)y}{1+a(x-m)}\,,\endaligned\tag1$$ where $x, y$ denote prey and predator population respectively at any time $t,d,k,\alpha,\beta,a,c,m$ are positive constants.

MSC 2000:: *34C60 Applications of qualitative theory of ODE
34C05 Qualitative theory of some special solutions of ODE
34D20 Lyapunov stability of ODE
92D25 Population dynamics

Keywords: predator-prey model; prey refuge; limit cycle; Holling type II; global stability

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Zentralblatt MATH Berlin [Germany]