I've been looking for the equilibrium point with the help of SymPy (Python Library). Even one of the equations cannot be found with SymPy because the solution is very long. I'm curious about the equilibrium point and stability of this system.
\begin{align*} \frac{dx_{1}}{dt} &= a_{1}+k_{7}x_{5}(\frac{x_{1}}{K+x_{1}})+k_{2}x_{1}x_{2}-d_{1}x_{1}-d_{7}x_{1}x_{5} \\ \frac{dx_{2}}{dt} &= a_{2}+k_{4}x_{4}-d_{2}x_{2}-k_{8}x_{2}x_{3} \\ \frac{dx_{3}}{dt} &= a_{3}x_{6}-d_{3}x_{3}-k_{1}x_{1}x_{3} \\ \frac{dx_{4}}{dt} &= a_{4}+k_{10}x_{3}-d_{6}x_{2}x_{4}-d_{4}x_{4}+k_{6}x_{6}-k_{3}x_{2} \\ \frac{dx_{5}}{dt} &= a_{5}-d_{5}x_{5} \\ \frac{dx_{6}}{dt} &= a_{6}x_{6}+a_{7}x_{5}-k_{5}x_{4}x_{6} \end{align*}