Skip to main content

Research Repository

See what's under the surface

Advanced Search

Existence and wandering of bumps in a spiking neural network model

Chow, Carson; Coombes, Stephen

Authors

Carson Chow



Abstract

We study spatially localized states of a spiking neuronal network populated by a pulse coupled phase oscillator known as the lighthouse model. We show that in the limit of slow synaptic interactions in the continuum limit the dynamics reduce to those of the standard Amari model. For non-slow synaptic connections we are able to go beyond the standard firing rate analysis of localized solutions allowing us to explicitly construct a family of co-existing one-bump solutions, and then track bump width and firing pattern as a function of system parameters. We also present an analysis of the model on a discrete lattice. We show that multiple width bump states can co-exist and uncover a mechanism for bump wandering linked to the speed of synaptic processing. Moreover, beyond a wandering transition point we show that the bump undergoes an effective random walk with a diffusion coefficient that scales exponentially with the rate of synaptic processing and linearly with the lattice spacing.

Journal Article Type Article
Publication Date May 1, 2006
Peer Reviewed Peer Reviewed
APA6 Citation Chow, C., & Coombes, S. (2006). Existence and wandering of bumps in a spiking neural network model
Keywords spiking neural network, bump solutions, working memory, lighthouse model
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

Files

LHsiads13.pdf (2 Mb)
PDF

Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





You might also like



Downloadable Citations

;