Simultaneous nonlinear equations of growth

The simultaneous equations

$$\begin{gathered} \frac{{dx}}{{dt}} = \frac{{a_x }}{{k_x }}k_x - x - f_x (y)] x \hfill \\ \frac{{dy}}{{dt}} = \frac{{a_y }}{{k_y }}k_y - y - f_y (x)] y \hfill \\ \end{gathered}$$