Figure 2

Time evolutions of the stochastic system with parameters \(S_{10}=1.5\), \(S_{20}=2\), \(Q=1.45\), \(\delta _{1}=0.9\), \(\delta _{2}=1\), \(a_{1}=1.6\), \(a_{2}=1.6\), \(\mu _{1}=0.8\), \(\mu _{2}=0.8\), \(r=0.1\), \(k=1\), \(g=0.8\), \(h=1\), \(m=0.2\), \(u=0.1\), \({T=1}\). (a) Time series for \(S_{1}(t)\), \(S_{2}(t)\), \(x(t)\) with parameters \(\sigma_{1}=0.6\), \(\sigma_{2}=0.9\), \(\mathcal{R}^{*}_{1} = 0.6759\). (b) Time series for \(S_{1}(t)\), \(S_{2}(t)\), \(x(t)\) with parameters \(\sigma_{1}=1\), \(\sigma_{2}=0.7\), \(\mathcal{R}^{*}_{2} = 0.6419\). (c) Time series for \(S_{1}(t)\), \(S_{2}(t)\), \(x(t)\) with parameters \(\sigma_{1}=1.5\), \(\sigma_{2}=1.6\), \(\mathcal{R}^{*}_{3} = 0.1830\). (d) Time series for \(S_{1}(t)\), \(S_{2}(t)\), \(x(t)\) with parameters \(\sigma_{1}=0.5\), \(\sigma_{2}=0.5\), \(\mathcal{R}^{*}_{4} = 0.9896\)