Waves, bumps, and patterns in neural field theories
Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analyti...
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| Format: | Article |
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2005
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| Online Access: | https://eprints.nottingham.ac.uk/153/ |
| _version_ | 1848790350764703744 |
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| author | Coombes, Stephen |
| author_facet | Coombes, Stephen |
| author_sort | Coombes, Stephen |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons. |
| first_indexed | 2025-11-14T18:11:13Z |
| format | Article |
| id | nottingham-153 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:11:13Z |
| publishDate | 2005 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-1532020-05-04T20:30:35Z https://eprints.nottingham.ac.uk/153/ Waves, bumps, and patterns in neural field theories Coombes, Stephen Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons. 2005-03 Article PeerReviewed Coombes, Stephen (2005) Waves, bumps, and patterns in neural field theories. bumps waves neural field theories integral equations Evans functions |
| spellingShingle | bumps waves neural field theories integral equations Evans functions Coombes, Stephen Waves, bumps, and patterns in neural field theories |
| title | Waves, bumps, and patterns in neural field theories |
| title_full | Waves, bumps, and patterns in neural field theories |
| title_fullStr | Waves, bumps, and patterns in neural field theories |
| title_full_unstemmed | Waves, bumps, and patterns in neural field theories |
| title_short | Waves, bumps, and patterns in neural field theories |
| title_sort | waves, bumps, and patterns in neural field theories |
| topic | bumps waves neural field theories integral equations Evans functions |
| url | https://eprints.nottingham.ac.uk/153/ |