  Critical dynamics of cortical neurons have been intensively studied over the
past decade. Neuronal avalanches provide the main experimental as well as
theoretical tools to consider criticality in such systems. Experimental studies
show that critical neuronal avalanches show mean-field behavior. There are
structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014)]
dynamical mechanisms which can lead to mean-field behavior. In this work we
consider a simple model of neuronal dynamics based on threshold self-organized
critical models with synaptic noise. We investigate the role of high average
connectivity, random long range connections, as well as synaptic noise in
achieving mean-field behavior. We employ finite-size scaling in order to
extract critical exponents with good accuracy. We conclude that relevant
structural mechanisms responsible for mean-field behavior cannot be justified
in realistic models of the cortex. However, strong dynamical noise, which can
have realistic justifications, always leads to mean-field behavior regardless
of the underlying structure. Our work provides a different (dynamical) origin
than the conventionaly accepted (structural) mechanisms for mean-field behavior
in neuronal avalanches.
