Figure 4

The boundary equilibrium state \(E_{1}=(1/8, 0)\) of (4) is a.s. locally asymptotically stable when \(\sigma _{1}=\sigma _{2}=0.9\), \(r_{1}=r_{2}=0.25\), \(a_{11}=2\), \(a_{12}= 0.6\), \(a_{21}=1\), and \(h=0.1\) satisfy \(2(r_{2}+\frac{a_{21}r_{1}}{a_{11}})-\sigma _{2}^{2}<0\), where the initial condition is \((u_{1}(0), u_{2}(0))=(0.5, 0.8)\)