A dynamical theory of spike train transitions in networks of integrate-and-fire oscillators
File(s)
Published version
Author(s)
Bressloff, PC
Coombes, S
Type
Journal Article
Abstract
A dynamical theory of spike train transitions in networks of pulse-coupled integrate-and-fire (IF) neural oscillators is presented. We begin by deriving conditions for 1:1 frequency- locking in a network with noninstantaneous synaptic interactions. This leads to a set of phase equations determining the relative firing times of the oscillators and the self-consistent collective period. We then investigate the stability of phase-locked solutions by constructing a linearized map of the firing times and analyzing its spectrum. We establish that previous results concerning the stability properties of IF oscillator networks are incomplete since they only take into account the effects of weak coupling instabilities. We show how strong coupling instabilities can induce transitions to nonphase locked states characterized by periodic or quasi-periodic variations of the interspike intervals on attracting invariant circles. The resulting spatio-temporal pattern of network activity is compatible with the behavior of a corresponding firing rate (analog) model in the limit of slow synaptic interactions.
Date Issued
2000-01
Date Acceptance
1999-03-25
Citation
SIAM Journal on Applied Mathematics, 2000, 60 (3), pp.820-841
ISSN
0036-1399
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Start Page
820
End Page
841
Journal / Book Title
SIAM Journal on Applied Mathematics
Volume
60
Issue
3
Copyright Statement
c 2000 Society for Industrial and Applied Mathematics
Identifier
http://dx.doi.org/10.1137/s0036139998339643
Publication Status
Published
Date Publish Online
2000-02-10