Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis
We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on...
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| Format: | Article |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/41032/ |
| _version_ | 1848796181438660608 |
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| author | Avitable, Daniele Wedgwood, Kyle C. A. |
| author_facet | Avitable, Daniele Wedgwood, Kyle C. A. |
| author_sort | Avitable, Daniele |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. Stationary and travelling bumps have similar meso- and macroscopic profiles, but different microscopic structure, hence we propose lifting operators which use microscopic motifs to disambiguate them. We provide numerical evidence that waves are supported by a combination of high synaptic gain and long refractory times, while meandering bumps are elicited by short refractory times. |
| first_indexed | 2025-11-14T19:43:54Z |
| format | Article |
| id | nottingham-41032 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:54Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-410322020-05-04T18:27:53Z https://eprints.nottingham.ac.uk/41032/ Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis Avitable, Daniele Wedgwood, Kyle C. A. We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on a continuum, we construct bumps and travelling waves analytically using standard interface methods from neural field theory. In a stochastic version with Heaviside firing rate, we construct approximate analytical probability mass functions associated with bumps and travelling waves. In the full stochastic model posed on a discrete lattice, where a coarse analytic description is unavailable, we compute patterns and their linear stability using equation-free methods. The lifting procedure used in the coarse time-stepper is informed by the analysis in the deterministic and stochastic limits. In all settings, we identify the synaptic profile as a mesoscopic variable, and the width of the corresponding activity set as a macroscopic variable. Stationary and travelling bumps have similar meso- and macroscopic profiles, but different microscopic structure, hence we propose lifting operators which use microscopic motifs to disambiguate them. We provide numerical evidence that waves are supported by a combination of high synaptic gain and long refractory times, while meandering bumps are elicited by short refractory times. Springer 2017-02-01 Article PeerReviewed Avitable, Daniele and Wedgwood, Kyle C. A. (2017) Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis. Journal of Mathematical Biology, 75 (4). pp. 885-928. ISSN 0303-6812 Multiple scale analysis ; Mathematical neuroscience ; Refractoriness ; Spatio-temporal patterns ; Equation-free modelling ; Markov chains http://link.springer.com/article/10.1007/s00285-016-1070-9 doi:10.1007/s00285-016-1070-9 doi:10.1007/s00285-016-1070-9 |
| spellingShingle | Multiple scale analysis ; Mathematical neuroscience ; Refractoriness ; Spatio-temporal patterns ; Equation-free modelling ; Markov chains Avitable, Daniele Wedgwood, Kyle C. A. Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis |
| title | Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis |
| title_full | Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis |
| title_fullStr | Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis |
| title_full_unstemmed | Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis |
| title_short | Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis |
| title_sort | macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis |
| topic | Multiple scale analysis ; Mathematical neuroscience ; Refractoriness ; Spatio-temporal patterns ; Equation-free modelling ; Markov chains |
| url | https://eprints.nottingham.ac.uk/41032/ https://eprints.nottingham.ac.uk/41032/ https://eprints.nottingham.ac.uk/41032/ |