  We have observed a new cataclysmic variable (CV) SDSS J080434.20+510349.2 and
study the origin of a long-term variability found in its light curve.
Multi-longitude time-resolved photometric observations were carried out to
analyze the uncommon behavior also found recently in two newly discovered CVs.
This study of SDSS J080434.20+510349.2 mainly concerns the understanding of the
nature of the observed double-humped light curve and its relation to a cyclic
brightening occurring during quiescence. The observations were obtained early
in 2007, when the object was at about V~17.1, 0.4 mag brighter than the
pre-outburst magnitude. The light curve shows a sinusoidal variability with an
amplitude of about 0.07 mag and a periodicity of 42.48 min, which is half of
the orbital period of the system. In addition, we have observed two
"mini-outbursts" of the system up to 0.6 mag, with a duration of about 4 days
each. The "mini-outburst" had a symmetric profile and repeated in about 32
days. Subsequent monitoring of the system shows a cyclical behaviour of such
"mini-outbursts" with a similar recurrence period. The origin of the
double-humped light curve and the periodic brightening is discussed in the
light of the evolutionary state of SDSS J080434.20+510349.2.
