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Koulakov,
Alexei Mean-field treatment of the network of Stevens-Zador neurons We apply a mean-field approach to the system of intergate-and-fire (IF) neurons with time varying resting potential and time constant [C. F. Stevens and A. M. Zador, Proc. of the 5th J. Symp. on Neur. Comp., UCSD, La Jolla, CA (1998)]. The network contains both inhibitory and excitatory neurons. In addition to the low frequency attractors found in the simple IF neurons we obtain a high frequency (>20 Hz) self-sustaining global state of the network. No external inputs are necessary to maintain this novel state. Such a state can therefore model the activity persistent after the removal of stimulus. For the high-frequency state to be stable the presence of inhibitory neurons is necessary. We derive the condition of stability and analyze the applicability of the mean-field approximation.
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