(10) \(\left\{\begin{matrix}\begin{matrix}\frac{dx(t)}{\text{dτ}}=\sigma\left(t\right)-\delta\left(t\right)x\left(t\right)+\rho(t)\frac{y\left(t\right)}{y\left(t\right)+\eta}-\mu x(t)y(t)\\ \frac{dy(t)}{\text{dτ}}=\alpha y\left(t\right)\left(1-\beta y\left(t\right)\right)-x\left(t\right)y\left(t\right)\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\\ \end{matrix}\\ \frac{d\sigma(t)}{\text{dτ}}=\mu_{\sigma}v_{v}\left(t\right)\left(1-\frac{\sigma(t)}{k_{\sigma}}\right)\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\\ \frac{d\delta(t)}{\text{dτ}}=\mu_{\delta}v_{v}\left(t\right)\left(1-\frac{\delta(t)}{k_{\delta}}\right)\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\\ \end{matrix}\right.\ \)
(11)
(12)
(13)