Measuring neuronal avalanches in disordered systems with absorbing states

Abstract

Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a system in which the separation of driving and relaxation time scales emerges from its structure. We apply both definitions of avalanche to our model. Both yield power-law-distributed avalanches that scale with system size in the critical point as expected. Nevertheless, we find restricted power-law-distributed avalanches outside of the critical region within the experimental procedure, which is not expected by the standard theoretical definition. We remark that these results are dependent on the model details.

21 pages, 7 figures

References in corpus (8)

• Emergent complex neural dynamics
• Dynamical synapses causing self-organized criticality in neural networks
• Self-Organized Criticality model for Brain Plasticity
• Spike Avalanches Exhibit Universal Dynamics across the Sleep-Wake Cycle
• Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks
• Quasi-Critical Brain Dynamics on a Non-Equilibrium Widom Line
• Neutral theory and scale-free neural dynamics
• Long-range epidemic spreading in a random environment

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