%0 Journal Article
%T Multiplicatively interacting point processes and applications to neural modeling
%A Stefano Cardanobile
%A Stefan Rotter
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0904.1505v3