Figure 2

The permanence of system ( 2.1 ) with \(\pmb{x(0)=0.1}\) , \(\pmb{y(0)=0.1}\) , \(\pmb{a=2}\) , \(\pmb{b=0.8}\) , \(\pmb{d_{1}=0.5}\) , \(\pmb{d_{2}=0.5}\) , \(\pmb{d_{3}=0.4}\) , \(\pmb{\beta_{1}=0.6}\) , \(\pmb{k_{1} =0.3}\) , \(\pmb{\beta _{2}=0.3}\) , \(\pmb{k_{2}=0.4}\) , \(\pmb{\mu=0.5}\) , \(\pmb{l=0.8}\) , \(\pmb{\tau=1}\) . (a) Time-series of \(x(t)\); (b) time-series of \(y(t)\); (c) the phase portrait of the permanence of system (2.1).