We study the dynamics of completely connected populations of refractory integrate-and-fire neurons in the presence of noise. Solving the master equation based on a mean-field approach, and by computer simulations, we find sustained states of activity that correspond to fixed points and show that for the same value of external input, the system has one or two attractors. The dynamic behavior of the population under the influence of external input and noise manifests hysteresis effects that might have a functional role for memory. The temporal dynamics at higher temporal resolution, finer than the transmission delay times and the refractory period, are characterized by synchronized activity of subpopulations. The global activity of the population shows aperiodic oscillations analogous to experimentally found field potentials.

The dynamic behavior of a network model consisting of all-to-all excitatory coupled binary neurons with global inhibition is studied analytically and numerically. We prove that for random input signals, the output of the network consists of synchronized bursts with apparently random intermissions of noisy activity. We introduce the fraction of simultaneously firing neurons as a measure for synchrony and prove that its temporal correlation function displays, besides a delta peak at zero indicating random processes, strongly dampened oscillations. Our results suggest that synchronous bursts can be generated by a simple neuronal architecture that amplifies incoming coincident signals. This synchronization process is accompanied by dampened oscillations that, by themselves, however, do not play any constructive role in this and can therefore be considered to be an epiphenomenon.