  The response of neurons is highly sensitive to the stimulus. The stimulus can
be associated with a direct injection in vitro experimentation (e.g., time
dependent and independent inputs); or post-synaptic potentials resulting from
the interaction of many neurons. A typical incoming stimulus resembles a noise
which in principle can be described as a random variable. In computational
neuroscience, the noise has been extensively studied for different setups. In
this study, we investigate the effect of noisy inputs in a minimal network of
two identical leaky integrate-and-fire (LIF) neurons interacting with finite
pulses. In particular, we consider a Gaussian white noise as a standard
function for stochastic modelling of neurons, while taking into account the
pulse width as an elementary component for the signal transmission. By
exploring the role of noise and finite pulses, the two neurons show a
synchronous spiking behaviour characterized by fluctuations in the interspike
intervals. Above some critical values the synchronous regime collapses onto
asynchronous dynamics. The abrupt change in such dynamics is accompanied by a
hysteresis, i.e., the coexistence of synchronous and asynchronous firing
behaviour.
