  We consider pulse-coupled Leaky Integrate-and-Fire neural networks with
randomly distributed synaptic couplings. This random dilution induces
fluctuations in the evolution of the macroscopic variables and deterministic
chaos at the microscopic level. Our main aim is to mimic the effect of the
dilution as a noise source acting on the dynamics of a globally coupled
non-chaotic system. Indeed, the evolution of a diluted neural network can be
well approximated as a fully pulse coupled network, where each neuron is driven
by a mean synaptic current plus additive noise. These terms represent the
average and the fluctuations of the synaptic currents acting on the single
neurons in the diluted system. The main microscopic and macroscopic dynamical
features can be retrieved with this stochastic approximation. Furthermore, the
microscopic stability of the diluted network can be also reproduced, as
demonstrated from the almost coincidence of the measured Lyapunov exponents in
the deterministic and stochastic cases for an ample range of system sizes. Our
results strongly suggest that the fluctuations in the synaptic currents are
responsible for the emergence of chaos in this class of pulse coupled networks.
