  The presence of both critical behavior and oscillating patterns in brain
dynamics is a very interesting issue. In this paper, we consider a model for a
neuron population, where each neuron is modeled by an over-damped rotator. We
find that in the space of external parameters, there exist some regions that
system shows synchronization. Interestingly, just at the transition point, the
avalanche statistics show a power-law behavior. Also, in the case of small
systems, the (partially) synchronization and power-law behavior can happen at
the same time.
