  The AM CVn systems are a class of He-rich, post-period minimum,
semi-detached, ultra-compact binaries. Their long-term light curves have been
poorly understood due to the few systems known and the long (hundreds of days)
recurrence times between outbursts. We present combined photometric light
curves from the LINEAR, CRTS, and PTF synoptic surveys to study the photometric
variability of these systems over an almost 10 yr period. These light curves
provide a much clearer picture of the outburst phenomena that these systems
undergo. We characterize the photometric behavior of most known outbursting AM
CVn systems and establish a relation between their outburst properties and the
systems' orbital periods. We also explore why some systems have only shown a
single outburst so far and expand the previously accepted phenomenological
states of AM CVn systems. We conclude that the outbursts of these systems show
evolution with respect to the orbital period, which can likely be attributed to
the decreasing mass transfer rate with increasing period. Finally, we consider
the number of AM CVn systems that should be present in modeled synoptic
surveys.
