  Scale-free behavior as well as oscillations are frequently observed in the
activity of many natural systems. One important example is the cortical tissues
of mammalian brain where both phenomena are simultaneously observed. Rhythmic
oscillations as well as critical (scale-free) dynamics are thought to be
important, but theoretically incompatible, features of a healthy brain.
Motivated by the above, we study the possibility of coexistence of scale-free
avalanches along with rhythmic behavior within the framework of self-organized
criticality. In particular, we add an oscillatory perturbation to local
threshold condition of the continuous Zhang model and characterize the
subsequent activity of the system. We observe regular oscillations embedded in
well-defined avalanches which exhibit scale-free size and duration in line with
observed neuronal avalanches. The average amplitude of such oscillations are
shown to decrease with increasing frequency consistent with real brain
oscillations. Furthermore, it is shown that optimal amplification of
oscillations occur at the critical point, further providing evidence for
functional advantages of criticality.
