  We study the equivalence between a nonlinear self-dual model (NSD) with the
Born-Infeld-Chern-Simons (BICS) models using an iterative gauge embedding
procedure that produces the duality mapping, including the case where the NSD
model is minimally coupled to dynamical, U(1) charged fermionic matter. The
duality mapping introduces a current-current interaction term while at the same
time the minimal coupling of the original nonlinear self-dual model is replaced
by a non-minimal magnetic like coupling in the BICS side.
