Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

TL;DR

This study shows that noisy local dynamics in a sandpile model can produce true criticality with mean-field exponents, resembling neuronal avalanches, despite breaking strict conservation.

Contribution

It demonstrates that noise can induce criticality in self-organized systems while preserving scale invariance, with exponents approaching mean-field values at high noise levels.

Findings

Criticality persists despite non-conservation due to noise.

Critical exponents approach mean-field values with increasing noise.

Critical behavior is confirmed in both 2D and 3D models.

Abstract

Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (non-conservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibit true criticality for a wide range of noise in various dimensions, given that conservation is respected \textit{on the average}. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, addition of noise does not affect the exponents at the upper critical dimension ($D=4$). In addition to extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method in order to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for general phenomena of criticality in non-equilibrium systems.