  We investigate the synaptic noise as a novel mechanism for creating critical
avalanches in the activity of neural networks. We model neurons and chemical
synapses by dynamical maps with a uniform noise term in the synaptic coupling.
An advantage of utilizing maps is that the dynamical properties (action
potential profile, excitability properties, post synaptic potential summation
etc.) are not imposed to the system, but occur naturally by solving the system
equations. We discuss the relevant neuronal and synaptic properties to achieve
the critical state. We verify that networks of excitatory by rebound neurons
with fast synapses present power law avalanches. We also discuss the measuring
of neuronal avalanches by subsampling our data, shedding light on the
experimental search for Self-Organized Criticality in neural networks.
