Figure 2

The numerical simulation of the impulsive system in Eq. (7) tends toward the periodically oscillatory solution \((0,\tilde{y}(t))\) using \(r=0.8\), \(k=0.5\), \(\beta =0.7\), \(a=0.3\), \(b=0.05\), \(\mu =0.85\), \(d=0.85\), \(\eta =0.1\), \(p_{1}=p_{2}=p_{3}=0.5\) when \((x(0),y(0))=(0.1,0.5)\) and \(T=2< T_{\max }=2.47\): (a) the time series simulation of the prey density \(x(t)\) approaching zero as t is sufficiently large; (b) the time series simulation of the predator density \(y(t)\) approaching a positive periodic solution as t is large enough; (c) the trajectory simulation plotted on the xy-plane