Skip to main content
  • Poster presentation
  • Open access
  • Published:

Modelling gap junctions in a neural field model

We study a nonlinear, one-dimensional neural field model based upon a partial integro-differential equation, that is used to model spatial patterns in working memory. Through the application of Fourier transforms to the PIDE, steady states of spatially localised areas of high activity can be represented by solutions of a fourth order ODE. Recent research has shown a high density of gap junctions in areas of the brain that experience epileptic events. We extend the model by including a diffusion-like term to model gap junctions and derive a sixth order ODE which we use to investigate changes in the dynamics of spatially localised solutions. We find that symmetric homoclinic orbits to a zero steady state exist for a wide area of parameter space. Numerical work shows families of solutions are destroyed as the strength of the term modelling gap junctions increases.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amanda Elvin.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Elvin, A. Modelling gap junctions in a neural field model. BMC Neurosci 8 (Suppl 2), P73 (2007). https://doi.org/10.1186/1471-2202-8-S2-P73

Download citation

  • Published:

  • DOI: https://doi.org/10.1186/1471-2202-8-S2-P73

Keywords