Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting

Figure 2

Phase portrait of the system (68) with 𝑟=8, 𝐾=10, 𝑎=0.8, 𝛽=0.5, 𝑏=0.3, ℎ=8, 𝑐=0.2, 𝜆=0.6, 𝑚=2, 𝑑_𝑆=0.2, 𝑑_𝐼=0.5, 𝑑_𝐽=0.4, 𝑑_𝑀=0.2, 𝛿=0.4, 𝑃_𝑆=𝑃_𝐼=𝑃_𝐽=𝑃_𝑀=0.2, 𝛿_𝐼=0.2, 𝛿_𝐽=0.3, 𝛿_𝑀=0.5, 𝜏=0.3, 𝑇=0.5, 𝑥(0)=20, 𝑆(0)=2, 𝐼(0)=2, 𝑦_𝐽(0)=0.5, 𝑦_𝑀(0)=0.5.

(a)

(b)