I am looking forward to solve the system of equations $$\frac{d x_i}{d t}=a_ix_i^2+b_ix_i-\sum\limits_{j\neq i}^nb_jx_j-d_i,$$ with $x_i\geq 0$, $a_i,b_i,c_i,d_i>0$ and $i\in[1,n]$.
Without the linear coupling term, the system reduces to a set of independent Riccati equations with constant coefficients that can be solved.
With the coupling, the system looks like a matrix equation but I don't know how to represent the quadratic term in matrix form.
Any kind of help for finding the solution, or link to literature would be very helpful.
Thank you!