On certain solvable systems of 4 nonlinear Ordinary Differential Equations

Some interesting (periodic!) solutions of certain systems of $4$ nonlinear Ordinary Differential Equations $d{x}_n\left(t\right)\mathrm{/}dt=P_2^{\left(n\right)}\left[x_m\left(t\right)\right]\mathrm{/}[x_1\left(t\right)+x_2\left(t\right)],n,m=1,2,3,4$, where $P_2^{\left(n\right)}\left[x_m\left(t\right)\right]$ are $4$ polynomials of degree $2$ in the $4$ dependent variables $x_m\left(t\right)$, are obtained.