  This paper studies the hydrodynamic limit of a stochastic process describing
the time evolution of a system with N neurons with mean-field interactions
produced both by chemical and by electrical synapses. This system can be
informally described as follows. Each neuron spikes randomly following a point
process with rate depending on its membrane potential. At its spiking time, the
membrane potential of the spiking neuron is reset to the value 0 and,
simultaneously, the membrane potentials of the other neurons are increased by
an amount of potential 1/N . This mimics the effect of chemical synapses.
Additionally, the effect of electrical synapses is represented by a
deterministic drift of all the membrane potentials towards the average value of
the system.
  We show that, as the system size N diverges, the distribution of membrane
potentials becomes deterministic and is described by a limit density which
obeys a non linear PDE which is a conservation law of hyperbolic type.
