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Allee effects in a predator--prey system with a saturated recovery function and harvesting

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Author(s): Mohammad javidi | N. Nyamoradi

Journal: International Journal of Advanced Mathematical Sciences
ISSN 2307-454X

Volume: 1;
Issue: 2;
Start page: 33;
Date: 2013;
Original page

ABSTRACT
In this paper, we will consider the Allee effects on predator--prey system with a saturated recovery function and harvesting. Local stability analysis of biologically feasible equilibrium points is worked out with help of ecological as well as disease basic reproduction numbers. We proved that the equilibrium $P_0=(0,0)$ of the predator--prey system  is (i) a saddle point in weak Allee effects (WAE) and (ii) asymptotically stable in strong Allee effects (SAE). We proved that the equilibrium $P_1=(eta,0)$ of the system is a saddle point if $R_0(1)1$ in SAE case. Also we proved that the equilibrium $P_2=(1,0)$ of the system  is a saddle point if $R_0(1)>1$ and asymptotically stability if $R_0(1)
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