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Figure 1 | Advances in Difference Equations

Figure 1

From: Analysis of a predator-prey model with impulsive diffusion and releasing on predator population

Figure 1

Globally asymptotically stable prey-extinction periodic solution of system ( 3 ) with \(\pmb{x_{1}(0)=0.5}\) , \(\pmb{y_{1}(0)=0.5}\) , \(\pmb{x_{2}(0)=0.5}\) , \(\pmb{y_{2}(0)=0.5}\) , \(\pmb{a_{1}=0.1}\) , \(\pmb{b_{1}=0.2}\) , \(\pmb{a_{2}=0.1}\) , \(\pmb{b_{2}=0.2}\) , \(\pmb{\beta_{1}=0.5}\) , \(\pmb{\beta_{2}=5}\) , \(\pmb{k_{1}=0.5}\) , \(\pmb{k_{2}=5}\) , \(\pmb{\mu_{1}=0.5}\) , \(\pmb{\mu_{2}=0.3}\) , \(\pmb{d_{1}=0.3}\) , \(\pmb{d_{2}=0.3}\) , \(\pmb{\sigma _{1}=3.5}\) , \(\pmb{\sigma_{2}=3.5}\) , \(\pmb{\tau=1}\) , \(\pmb{l=0.25}\) , \(\pmb{D=0.1}\) . (a) Time-series of \(x_{1}(t)\); (b) Time-series of \(y_{1}(t)\); (c) Time-series of \(x_{2}(t)\); (d) Time-series of \(y_{2}(t)\).

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