Figure 3

Dynamical behavior of (1.2). (a) is for system (1.2) with \(\xi _{1}=0.4\), \(\xi _{2}=0.8\), \(\xi _{3}=0.01\), then \(N_{2}(t)\) is extinct, and \(\lim_{t\rightarrow \infty }\langle N_{1}(t)\rangle =0.1671\), \(\lim_{t\rightarrow \infty }\langle N_{3}(t)\rangle =0.5123\). (b) is for system (1.2) with \(r_{3}=0.1\), \(\xi _{1}=0.469\), \(\xi _{2}=0.8\), \(\xi _{3}=0.01\), then \(N_{2}(t)\), \(N_{3}(t)\) are both extinct and \(\lim_{t\rightarrow \infty }\langle N_{1}(t)\rangle =0.5\)