  We introduce a nonlinear modification of the classical Hawkes process, which
allows inhibitory couplings between units without restrictions. The resulting
system of interacting point processes provides a useful mathematical model for
recurrent networks of spiking neurons with exponential transfer functions. The
expected rates of all neurons in the network are approximated by a first-order
differential system. We study the stability of the solutions of this equation,
and use the new formalism to implement a winner-takes-all network that operates
robustly for a wide range of parameters. Finally, we discuss relations with the
generalised linear model that is widely used for the analysis of spike trains.
