Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator

Figure 2

For ((a) and (b)) , , . (a) : the interior equilibrium point is asymptotically stable, axial equilibrium point is asymptotically stable, and interior equilibrium point is a saddle point. (b) : the point is unstable, is asymptotically stable, and is a saddle. (c) , , , and : the interior equilibrium point is asymptotically stable; axial equilibrium point is saddle. (d) , , , and : the interior equilibrium point is asymptotically stable; axial equilibrium point is saddle. (e) The phase portrait diagram when no interior equilibrium exists. The origin is always a saddle.

(a)

(b)

(c)

(d)

(e)