  The dynamical fermion mass generation on a 3-brane in the 5D space-time is
discussed in a model with bulk fermions in interaction with fermions on the
brane assuming the presence of a constant abelian gauge field component $A_5$
in the bulk. We calculate the effective potential as a function of the fermion
masses and the gauge field component $A_5$. The masses can be found from the
stationarity condition for the effective potential (the gap equation). We
formulate the equation for the mass spectrum of the 4D--fermions. The phases
with finite and vanishing fermion masses are studied and the dependence of the
masses on the radius of the 5th dimension is analyzed. The influence of the
$A_5$-component of the gauge field on the symmetry breaking is considered both
when this field is a background parameter and a dynamical variable. The
critical values of the $A_5$ field, the coupling constant and the radius are
examined.
