  We present a numerical study of the impact of AGN accretion and feedback on
the star formation history of barred disc galaxies. Our goal is to determine
whether the effect of feedback is positive (enhanced star formation) or
negative (quenched star formation), and to what extent. We performed a series
of 12 hydrodynamical simulations of disc galaxies, 10 barred and 2 unbarred,
with various initial gas fractions and AGN feedback prescriptions. In barred
galaxies, gas is driven toward the centre of the galaxy and causes a starburst,
followed by a slow decay, while in unbarred galaxies the SFR increases slowly
and steadily. AGN feedback suppresses star formation near the central black
hole. Gas is pushed away from the black hole, and collides head-on with
inflowing gas, forming a dense ring at a finite radius where star formation is
enhanced. We conclude that both negative and positive feedback are present, and
these effects mostly cancel out. There is no net quenching or enhancement in
star formation, but rather a displacement of the star formation sites to larger
radii. In unbarred galaxies, where the density of the central gas is lower,
quenching of star formation near the black hole is more efficient, and
enhancement of star formation at larger radii is less efficient. As a result,
negative feedback dominates. Lowering the gas fraction reduces the star
formation rate at all radii, whether or not there is a bar or an AGN.
