Figure 1

Simulation of the species \(\pmb{x_{1}(t)}\) , \(\pmb{x_{2}(t)}\) under stochastic environment. Some paraments are taken: \(r_{1}=0.5\), \(r_{2}=0.05\), \(E_{1}=0.4\), \(E_{2}=0.02\), \(b_{1}=0.5\), \(b_{2}=0.6\), \(D_{1}=0.4\), \(D_{2}=0.3\), \(d_{1}=0.1\), \(d_{2}=0.01\), \(\tau_{1}=2\), \(\tau _{2}=1\); \(\alpha_{1}=0.4\), \(\alpha_{2}=0.3\), \(\xi_{1}(\theta)=0.3+0.03\sin\theta\), \(\xi _{2}(\theta)=0.1+0.05\cos\theta\), \(\theta\in[-2,0]\). (a) \(\sigma_{11}=\sigma_{12}=\sigma_{21}=\sigma_{22}\equiv0\); (b) \(\sigma_{11}=0.3\), \(\sigma_{12}=0.4\), \(\sigma_{21}=0.15\), \(\sigma _{22}=0.2\); (c) \(\sigma_{11}=0.02\), \(\sigma_{12}=0.01\), \(\sigma_{21}=0.3\), \(\sigma_{22}=0.3\); (d) \(\sigma_{11}=0.02\), \(\sigma_{12}=0.01\), \(\sigma_{21}=0.01\), \(\sigma_{22}=0.02\).