2020/03/06 by Johannes Pausch, Pausch, Johannes, Rosalba Garcia-Millan +3
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2003.03302
openalex publication_date 2020/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, neuronal avalanches have been observed to display oscillations, a\nphenomenon regarded as the co-existence of a scale-free behaviour (the\navalanches close to criticality) and scale-dependent dynamics (the\noscillations). Ordinary continuous-time branching processes with constant\nextinction and branching rates are commonly used as models of neuronal\nactivity, yet they lack any such time-dependence. In the present work, we\nextend a basic branching process by allowing the extinction rate to oscillate\nin time as a new model to describe cortical dynamics. By means of a\nperturbative field theory, we derive relevant observables in closed form. We\nsupport our findings by quantative comparison to numerics and qualitative\ncomparison to available experimental results.\n