On the validity of solutions and equilibrium points in a nonlinear network

For constrained differential equations arising in a specific nonlinear network, the inconsistency between two seemingly equivalent unconstrained representations has been long debated in the literature. One of the representations has nonunique solutions which violate the network constraints. Using new analytical tools, this brief proves that the two representations are not equivalent. Also the "explanations" for the discrepancy which appeared recently are incorrect as such, but can be restated precisely.