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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 \(m\)
\[ \begin{aligned} & \dot x=\alpha x\left(1-\frac xk\right)-\frac{\beta(x-m)y}{1+a(x-m)}\,,\\ & \dot y=-dy + \frac{c\beta(x-m)y}{1+a(x-m)}\,,\end{aligned}\tag{1} \]
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 ordinary differential equation models
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
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References:
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