Time-dependent branching processes: a model of oscillating neuronal avalanches

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Pausch, Johannes 
Garcia-Millan, Rosalba 
Pruessner, Gunnar 

Abstract: 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 quantitative comparison to numerics and qualitative comparison to available experimental results.


Funder: Engineering and Physical Sciences Research Council; doi: http://dx.doi.org/10.13039/501100000266

Article, /631/378/3920, /639/766/530/2795, /639/766/530/2804, article
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Scientific Reports
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Nature Publishing Group UK