Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary continuous-time branching processes with constant extinction and branching rates are commonly used as models of neuronal activity, yet they lack any such time-dependence. In the present work, we extend a basic branching process by allowing the extinction rate to oscillate in time as a new model to describe cortical dynamics. By means of a perturbative field theory, we derive relevant observables in closed form. We support our findings by quantative comparison to numerics and qualitative comparison to available experimental results.
@article{arxiv.2003.03302,
title = {Time-dependent branching processes: a model of oscillating neuronal avalanches},
author = {Johannes Pausch and Rosalba Garcia-Millan and Gunnar Pruessner},
journal= {arXiv preprint arXiv:2003.03302},
year = {2020}
}