##
Abstract

Perfect spike-to-spike synchrony is studied in all-to-all coupled
networks of identical excitatory, current-based, integrate-and-fire
neurons with delta-impulse coupling currents and Poisson spike-train
external drive. This synchrony is induced by repeated cascading
*total firing events*, during which all neurons fire at once. In this
regime, the network exhibits nearly periodic dynamics, switching between
an effectively uncoupled state and a cascade-coupled total firing state.
The probability of cascading total firing events occurring in the
network is computed through a combinatorial analysis conditioned upon
the random time when the first neuron fires and using the probability
distribution of the subthreshold membrane potentials for the remaining
neurons in the network. The probability distribution of the former is
found from a first-passage-time problem described by a Fokker-Planck
equation, which is solved analytically via an eigenfunction expansion.
The latter is found using a central limit argument via a calculation of
the cumulants of a single neuronal voltage. The influence of additional
physiological effects that hinder or eliminate cascade-induced synchrony
are also investigated. Conditions for the validity of the
approximations made in the analytical derivations are discussed and
verified via direct numerical simulations.

Click here
to download a preprint of this paper.

This work was partly supported by the National Science
Foundation through grants DMS-0506287 and DMS-0636358.

Back to Gregor Kovacic's
Home Page