Coexistence of scale invariant and rhythmic behavior in self-organized criticality

TL;DR

This paper demonstrates that scale-free avalanches and rhythmic oscillations can coexist in self-organized critical systems, with oscillation amplitude influenced by frequency and optimized at criticality, mirroring brain activity.

Contribution

It introduces a model showing coexistence of scale-invariant avalanches and rhythmic oscillations, highlighting the critical point as optimal for oscillation amplification.

Findings

Oscillations embedded in avalanches exhibit scale-free size and duration.

Oscillation amplitude decreases with increasing frequency.

Maximum oscillation amplification occurs at the critical point.

Abstract

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.