\frac{dx_{1}}{dt} = \left(k_{1} \cdot \left(1 - x_{1} / k_{5}\right) - k_{2} \cdot x_{2}\right) \cdot x_{1}\\
\frac{dx_{2}}{dt} = \left(\left(-k_{3}\right) + k_{4} \cdot x_{1}\right) \cdot x_{2}