Continuation of localised coherent structures in nonlocal neural field equations
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...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Published: |
Society for Industrial and Applied Mathematics
2014
|
| Online Access: | https://eprints.nottingham.ac.uk/2327/ |
| _version_ | 1848790756180885504 |
|---|---|
| author | Rankin, James Avitabile, Daniele Baladron, Javier Faye, Gregory Lloyd, David J.B. |
| author_facet | Rankin, James Avitabile, Daniele Baladron, Javier Faye, Gregory Lloyd, David J.B. |
| author_sort | Rankin, James |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:17:40Z |
| format | Article |
| id | nottingham-2327 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:17:40Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-23272020-05-04T20:17:40Z https://eprints.nottingham.ac.uk/2327/ Continuation of localised coherent structures in nonlocal neural field equations Rankin, James Avitabile, Daniele Baladron, Javier Faye, Gregory Lloyd, David J.B. 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. Society for Industrial and Applied Mathematics 2014 Article PeerReviewed Rankin, James, Avitabile, Daniele, Baladron, Javier, 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 http://epubs.siam.org/doi/abs/10.1137/130918721 doi:10.1137/130918721 doi:10.1137/130918721 |
| spellingShingle | Rankin, James Avitabile, Daniele Baladron, Javier Faye, Gregory Lloyd, David J.B. Continuation of localised coherent structures in nonlocal neural field equations |
| title | Continuation of localised coherent structures in nonlocal neural field equations |
| title_full | Continuation of localised coherent structures in nonlocal neural field equations |
| title_fullStr | Continuation of localised coherent structures in nonlocal neural field equations |
| title_full_unstemmed | Continuation of localised coherent structures in nonlocal neural field equations |
| title_short | Continuation of localised coherent structures in nonlocal neural field equations |
| title_sort | continuation of localised coherent structures in nonlocal neural field equations |
| url | https://eprints.nottingham.ac.uk/2327/ https://eprints.nottingham.ac.uk/2327/ https://eprints.nottingham.ac.uk/2327/ |