Continuation of localised coherent structures in nonlocal neural field equations

Rankin, James and Avitabile, Daniele and Baladron, Javier and Faye, Gregory and Lloyd, David J.B. (2014) Continuation of localised coherent structures in nonlocal neural field equations. SIAM Journal on Scientific Computing, 36 (1). B70-B93. ISSN 1064-8275

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Abstract

We study localised activity patterns in neural field equations posed on the Euclidean plane; such models are commonly used to describe the coarse-grained activity of large ensembles of cortical neurons in a spatially continuous way. We employ matrix-free Newton-Krylov

solvers and perform numerical continuation of localised patterns directly on the integral form of the equation. This opens up the possibility to study systems whose synaptic kernel does not lead to an equivalent PDE formulation. We present a numerical bifurcation study of localised states and show that the proposed models support

patterns of activity with varying spatial extent through the

mechanism of homoclinic snaking. The regular organisation of these patterns is due to spatial interactions at a specific scale associated with the separation of excitation peaks in the chosen connectivity function. The results presented form a basis for the general study of localised cortical activity with inputs and, more specifically, for investigating the localised spread of orientation selective activity that has been observed in the primary visual cortex with local visual input.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1137/130918721
Depositing User: Avitabile, Dr. Daniele
Date Deposited: 17 Mar 2014 00:17
Last Modified: 13 Sep 2016 23:38
URI: http://eprints.nottingham.ac.uk/id/eprint/2327

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