Time-dependent branching processes: a model of oscillating neuronal avalanches.
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Pausch, J., Garcia-Millan, R., & Pruessner, G. (2020). Time-dependent branching processes: a model of oscillating neuronal avalanches.. Scientific reports, 10 (1), 13678. https://doi.org/10.1038/s41598-020-69705-5
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.
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External DOI: https://doi.org/10.1038/s41598-020-69705-5
This record's URL: https://www.repository.cam.ac.uk/handle/1810/308036
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