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Theory and Modern Applications

Figure 4 | Advances in Difference Equations

Figure 4

From: Dynamics of a predator-prey model with impulsive biological control and unilaterally impulsive diffusion

Figure 4

Globally asymptotically stable prey-extinction periodic solution \(\pmb{(0,\widetilde{y_{1}(t)},\widetilde{y_{2}(t)})}\) of System ( 2.1 ) with \(\pmb{x_{1}(0)=0.5}\) , \(\pmb{y_{1}(0)=0.5}\) , \(\pmb{y_{2}(0)=0.5}\) , \(\pmb{a_{1}=2.4}\) , \(\pmb{b_{1}=0.1}\) , \(\pmb{a_{2}=1.5}\) , \(\pmb{b_{2}=0.21}\) , \(\pmb{\beta_{1}=0.3}\) , \(\pmb{k_{1}=0.5}\) , \(\pmb{\mu=0.86}\) , \(\pmb{d_{1}=0.1}\) , \(\pmb{\tau=1}\) , \(\pmb{l=0.25}\) , \(\pmb{D=0.6}\) . (a) Time-series of \(x_{1}(t)\); (b) time-series of \(y_{1}(t)\); (c) time-series of \(y_{2}(t)\); (d) the phase portrait of globally asymptotically stable periodic solution \((0,\widetilde{y_{1}(t)},\widetilde{y_{2}(t)})\) of System (2.1).

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