This question had been clarified only in the 35bd3dee8abe5e1dee9966" title="Click to view the MathML source">d=2 equations case. For d≥3 equations, prior to the present paper, only very restrictive results were known, namely when the above system was a small perturbation of the super-symmetrical case 35b446b747a" title="Click to view the MathML source">λi≡λ and 351adf6fb700d74" title="Click to view the MathML source">bij≡b. We treat the general case, uncovering in particular a much more complex and richer structure with respect to the 35bd3dee8abe5e1dee9966" title="Click to view the MathML source">d=2 case.