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Theory and Modern Applications

Figure 3 | Advances in Difference Equations

Figure 3

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

Figure 3

Globally asymptotically stable prey-extinction periodic solution \(\pmb{(0,\widehat{y_{1}(t)},0)}\) of System ( 2.1 ) with \(\pmb{x_{1}(0)=0.5}\) , \(\pmb{y_{1}(0)=0.5}\) , \(\pmb{y_{2}(0)=0.5}\) , \(\pmb{a_{1}=2.4}\) , \(\pmb{b_{1}=0.1}\) , \(\pmb{a_{2}=1.5}\) , \(\pmb{b_{2}=0.21}\) , \(\pmb{\beta_{1}=0.3}\) , \(\pmb{k_{1}=0.5}\) , \(\pmb{\mu=0.86}\) , \(\pmb{d_{1}=0.1}\) , \(\pmb{\tau=1}\) , \(\pmb{l=0.25}\) , \(\pmb{D=0.78}\) . (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 \((0,\widehat{y_{1}(t)},0)\) of System (2.1).

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