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

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In this paper, we will consider the Allee effects onpredator--prey system with a saturated recovery function andharvesting. Local stability analysis of biologically feasibleequilibrium points is worked out with help of ecological as wellas disease basic reproduction numbers. We proved that theequilibrium $P_0=(0,0)$ of the predator--prey system is (i) asaddle point in weak Allee effects (WAE) and (ii) asymptoticallystable in strong Allee effects (SAE). We proved that theequilibrium $P_1=(\beta,0)$ of the system is a saddle point if$R_0(1)<1$ and unstable if $R_0(1)>1$ in SAE case. Also we provedthat the equilibrium $P_2=(1,0)$ of the system is a saddle pointif $R_0(1)>1$ and asymptotically stability if $R_0(1)<1$ in SAEcase. It is shown that the coexistence equilibria is notasymptotically stable. Numerical simulations are carried out fora hypothetical set of parameter values to substantiate our
    analytical findings.

 

View

Download

Article ID: 735
 
DOI: 10.14419/ijams.v1i2.735




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.