Dynamics of strongly coupled spiking neurons

We present a dynamical theory of integrate-and-fire neurons with strong syn aptic coupling. We show how phase-locked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to s tates characterized by spatiotemporal variations in the interspike interval s (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean fir ing rates. A fundamental result is that for slow interactions, there is goo d agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are pr esented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Secon d, an asymmetric network with a mixture of excitation and inhibition is sho wn to exhibit periodic bursting patterns. Finally, a one-dimensional networ k of neurons with long-range interactions is shown to desynchronize to a st ate with a spatially periodic pattern of mean firing rates across the netwo rk. This is modulated by deterministic fluctuations of the instantaneous fi ring rate whose size is an increasing function of the speed of synaptic res ponse.