Figure 1

The sample paths of three-species densities. (a) The sample paths of \(x_{i}(t), i=1,2,3\). The parameter values used in Example 5.1; (b) Under the control \(\hat{u}_{1}=(-\sqrt{x_{2}}\frac{2(x_{1}-3)}{x_{1}},-\sqrt{x_{3}}\frac {2(x_{2}-1)}{x_{2}}, -\sqrt{x_{1}}\frac{2(x_{3}-2)}{x_{3}})\), the sample paths of \(x_{i}(t), i=1,2,3\). The parameter values used in Example 5.2; (c) Under the \(\hat{u}_{2}=(-\sqrt{x_{2}}\frac{2(x_{1}-3)}{x_{1}},0,0)\), the sample paths of \(x_{i}(t), i=1,2,3\). the parameter values used in Example 5.3.