Figure 4

Graph of function \(S_{0}\) (a). The positive equilibrium \(E^{*}\) of system (1.2) is unstable when \(\tau=1\) (b), \(\tau=2.65\) (d), and stable when \(\tau=2\) (c). The other parameter values are \(r=0.11\), \(K=10\), \(\beta=0.2\), \(a=0.12\), \(h_{1}=0.01\), \(h_{2}=0.01\), \(m=0.15\), \(\theta=6\), and \(\varepsilon=0.7\). The initial condition for panels (b) and (c) is \(x_{0}=8\), \(y_{0}=5\). Multiple initial conditions are used for panels (d)