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Theory and Modern Applications

Figure 1 | Advances in Difference Equations

Figure 1

From: Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

Figure 1

Time series simulations of the impulsive system in Eq. (7) using \(r=3.1\), \(k=2.067\), \(\beta =1.083\), \(a=1.031\), \(b=0.001\), \(\mu =0.85\), \(d=0.3\), \(\eta =0.01\): (a) without taking any impulsive control strategy \((p_{1}=p_{2}=p_{3}=0)\) when \((x(0),y(0))=(0.5,0.5)\) and \(T=13\); (b) with only releasing the predators \((p_{1}=p_{2}=0, p_{3}=0.8)\) when \((x(0),y(0))=(1,1)\) and \(T=0.8< T_{\max }=0.9\); (c) with applying the IPM strategy \((p_{1}=0.85, p_{2}=0.2, p_{3}=0.9)\) when \((x(0),y(0))=(1,1)\) and \(T=1< T_{\max }=1.335\)

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