Figure 2

Globally asymptotically stable phytoplankton-extinction periodic solution of system (2.1) with \(s(0)=0.3\), \(x_{1}(0)=0.3\), \(x_{2}(0)=0.3\), \(\lambda _{1}=0.5\), \(d_{1}=0.2\), \(\beta _{11}=0.5\), \(\delta _{11}=1\), \(\beta _{12}=0.5\), \(\delta _{12}=1\), \(d_{11}=0.4\), \(d_{12}=0.4\), \(\lambda _{2}=0.1\), \(d_{2}=0.2\), \(\beta _{21}=0.3\), \(\delta _{21}=1\), \(\beta _{22}=0.3\), \(\delta _{22}=1\), \(d_{21}=0.3\), \(d_{22}=0.3\), \(E_{s}=0.3\), \(E_{1}=0.2\), \(E_{2}=0.2\), \(\mu _{s}=0.28\), \(\mu _{1}=0.1\), \(\mu _{2}=0.1\), \(\mu =0.1\), \(l=0.8\), \(\tau =1\); (a) time-series of \(s(t)\); (b) time-series of \(x_{1}(t)\); (c) time-series of \(x_{1}(t)\); (d) the phase portrait of the globally asymptotically stable phytoplankton-extinction periodic solution of system (2.1)