Figure 3

Graph of function \(S_{0}\) (a). The positive equilibrium \(E^{*}\) of system (1.2) is stable when \(\tau=0.9\) (b), and unstable when \(\tau=3\) (c), \(\tau=6\) (d). The other parameter values are \(r=0.11\), \(K=10\), \(\beta=0.3\), \(a=0.12\), \(h_{1}=0.01\), \(h_{2}=0.01\), \(m=0\), \(\theta=6\), and \(\varepsilon=0.7\). Here the initial condition is \(x_{0}=8\), \(y_{0}=5\)