Figure 5

Permanence for System ( 2.1 ) with \(\pmb{x_{1}(0)=0.5}\) , \(\pmb{y_{1}(0)=0.5}\) , \(\pmb{y_{2}(0)=0.5}\) , \(\pmb{a_{1}=4}\) , \(\pmb{b_{1}=0.1}\) , \(\pmb{a_{2}=4}\) , \(\pmb{b_{2}=0.21}\) , \(\pmb{\beta_{1}=0.3}\) , \(\pmb{k_{1}=0.1}\) , \(\pmb{\mu=0.01}\) , \(\pmb{d_{1}=0.1}\) , \(\pmb{\tau=1}\) , \(\pmb{l=0.25}\) , \(\pmb{D=0.01}\) . (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 permanence for System (2.1).