Ayt�l G�k�e
Neural Fields: Localised States with Piece-Wise Constant Interactions
G�k�e, Ayt�l; Coombes, Stephen; Avitabile, Daniele
Authors
Professor Stephen Coombes STEPHEN.COOMBES@NOTTINGHAM.AC.UK
PROFESSOR OF APPLIED MATHEMATICS
Daniele Avitabile
Abstract
Neural field models are typically cast as continuum integro-differential equations for describing the idealised coarse-grained activity of populations of interacting neurons. For smooth Mexican hat kernels, with short-range excitation and long-range inhibition, these non-local models can support various localised states in the form of spots in two-dimensional media. In recent years, there has been a growing interest in the mathematical neuroscience community in studying such models with a Heaviside firing rate non-linearity, as this often allows substantial insight into the stability of stationary solutions in terms of integrals over the kernels. Here we consider the use of piece-wise constant kernels that allow the explicit evaluation of such integrals. We use this to show that azimuthal instabilities are not possible for simple piece-wise constant Top Hat interactions, whilst they are easily realised for piece-wise constant Mexican hat interactions.
Citation
Gökçe, A., Coombes, S., & Avitabile, D. (2018). Neural Fields: Localised States with Piece-Wise Constant Interactions. In Mathematical and Theoretical Neuroscience: Cell, Network and Data Analysis (111-121). Springer Nature. https://doi.org/10.1007/978-3-319-68297-6_7
Publication Date | Mar 21, 2018 |
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Deposit Date | Nov 19, 2018 |
Electronic ISSN | 2281-5198 |
Publisher | Springer Nature |
Volume | 24 |
Pages | 111-121 |
Series Title | Springer INdAM Series |
Series ISSN | 2281-5198 |
Book Title | Mathematical and Theoretical Neuroscience: Cell, Network and Data Analysis |
ISBN | 978-3-319-68297-6 |
DOI | https://doi.org/10.1007/978-3-319-68297-6_7 |
Public URL | https://nottingham-repository.worktribe.com/output/1217573 |
Publisher URL | https://link.springer.com/chapter/10.1007%2F978-3-319-68297-6_7 |
Contract Date | Mar 21, 2018 |
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