A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics
Abstract
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in BMS. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (``raster plots''). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.
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