Modelling and Analysis of a Pest-Control Pollution Model with Integrated Control Tactics

Figure 4

Dynamical behavior (permanence) of system (2.1) with 𝑎=0.8, 𝑏₁=0.9, 𝜏=0.7, 𝑓=0.2, 𝛽=0.9, 𝜂=1, 𝑟=0.7, 𝑏₂=0.3, 𝜆=0.9, 𝑘=1, 𝑔=0.5, 𝑚=0.7, ℎ=2, 𝑙=0.1, 𝑇=2, and 𝜇₂=0.1, initial values 𝑥_𝑗(0)=0.2, 𝑥(0)=0.1, 𝑦(0)=0.1, 𝑐_𝑜(𝑡)=0.01, and 𝑐_𝑒(𝑡)=0.01 (^∗corresponding theoretical criteria value:  𝜇₁^∗∗=0.1654. (a) Time-series of system (2.1) with 𝜇₁=0.12. (b) Solution 𝑥_𝑗(𝑡),𝑥(𝑡),𝑦(𝑡) with 𝜇₁=0.12 will finally tend to a 𝑇-periodic solution.

(a)

(b)