Synchronization, oscillations, and 1/f noise in networks of spiking neurons
We investigate a model for neural activity that generates long range temporal correlations, 1/ f noise, and oscillations in global activity. The model consists of a two-dimensional sheet of leaky integrate-and- fire neurons with feedback connectivity consisting of local excitation and surround inhibition. Each neuron is independently driven by homogeneous external noise. Spontaneous symmetry breaking occurs, resulting in the formation of "hotspots" of activity in the network. These localized patterns of excitation appear as clusters that coalesce, disintegrate, or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters. The emergent cross-correlation functions have a dual structure, with a sharp peak around zero on top of a much broader hill. The power spectrum associated with single units shows a 1/ f decay for small frequencies and is flat at higher frequencies, while the power spectrum of the spiking activity averaged over many cells-equivalent to the local field potential-shows no 1/ f decay but a prominent peak around 40 Hz.
© 1994 Morgan Kaufmann. We are indebted to William Softky, Wyeth Bair, Terry Sejnowski, Michael Cross, John Hopfield, and Ernst Niebur, for insightful discussions. Our research was supported by a Myron A. Bantrell Research Fellowship, the Howard Hughes Medical Institute, the National Science Foundation, the Office of Naval Research and the Air Force Office of Scientific Research.
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