Snakes and ladders in an inhomogeneous neural field model
Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic modulation of the synaptic connectivity kernel and find tha...
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| Format: | Article |
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Elsevier
2014
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| Online Access: | https://eprints.nottingham.ac.uk/27873/ |
| _version_ | 1848793460258111488 |
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| author | Avitabile, Daniele Schmidt, Helmut |
| author_facet | Avitabile, Daniele Schmidt, Helmut |
| author_sort | Avitabile, Daniele |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with
periodic modulation of the synaptic connectivity kernel and find that they are arranged in a snakes-and-ladders bifurcation structure. In the case of Heaviside firing rates, we construct analytically symmetric and asymmetric states and hence derive closed-form expressions for the corresponding bifurcation diagrams. We show that the ideas proposed by Beck and co-workers to analyze snaking solutions to the Swift--Hohenberg equation remain valid for the neural field model, even though the corresponding spatial-dynamical formulation is non-autonomous. We investigate how the modulation amplitude affects the bifurcation structure and compare numerical calculations for steep sigmoidal firing rates with analytic predictions valid in the Heaviside limit. |
| first_indexed | 2025-11-14T19:00:39Z |
| format | Article |
| id | nottingham-27873 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:00:39Z |
| publishDate | 2014 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-278732020-05-04T20:16:07Z https://eprints.nottingham.ac.uk/27873/ Snakes and ladders in an inhomogeneous neural field model Avitabile, Daniele Schmidt, Helmut Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic modulation of the synaptic connectivity kernel and find that they are arranged in a snakes-and-ladders bifurcation structure. In the case of Heaviside firing rates, we construct analytically symmetric and asymmetric states and hence derive closed-form expressions for the corresponding bifurcation diagrams. We show that the ideas proposed by Beck and co-workers to analyze snaking solutions to the Swift--Hohenberg equation remain valid for the neural field model, even though the corresponding spatial-dynamical formulation is non-autonomous. We investigate how the modulation amplitude affects the bifurcation structure and compare numerical calculations for steep sigmoidal firing rates with analytic predictions valid in the Heaviside limit. Elsevier 2014 Article NonPeerReviewed Avitabile, Daniele and Schmidt, Helmut (2014) Snakes and ladders in an inhomogeneous neural field model. Physica D: Nonlinear Phenomena . ISSN 0167-2789 (In Press) Neural fields; Bumps; Localized states; Snakes and ladders; Inhomogeneities http://www.journals.elsevier.com/physica-d-nonlinear-phenomena/ |
| spellingShingle | Neural fields; Bumps; Localized states; Snakes and ladders; Inhomogeneities Avitabile, Daniele Schmidt, Helmut Snakes and ladders in an inhomogeneous neural field model |
| title | Snakes and ladders in an inhomogeneous neural field model |
| title_full | Snakes and ladders in an inhomogeneous neural field model |
| title_fullStr | Snakes and ladders in an inhomogeneous neural field model |
| title_full_unstemmed | Snakes and ladders in an inhomogeneous neural field model |
| title_short | Snakes and ladders in an inhomogeneous neural field model |
| title_sort | snakes and ladders in an inhomogeneous neural field model |
| topic | Neural fields; Bumps; Localized states; Snakes and ladders; Inhomogeneities |
| url | https://eprints.nottingham.ac.uk/27873/ https://eprints.nottingham.ac.uk/27873/ |