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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Main Authors:	Avitable, Daniele, Wedgwood, Kyle C. A.
Format:	Article
Language:	English English
Published:	Springer 2017
Online Access:	http://eprints.nottingham.ac.uk/41032/ http://eprints.nottingham.ac.uk/41032/ http://eprints.nottingham.ac.uk/41032/ http://eprints.nottingham.ac.uk/41032/8/Coherent%2010.1007_s00285-016-1070-9.pdf http://eprints.nottingham.ac.uk/41032/1/1603.04486.pdf

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recordtype	eprints
spelling	nottingham-410322018-06-12T04:12:37Z http://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 application/pdf en cc_by http://eprints.nottingham.ac.uk/41032/8/Coherent%2010.1007_s00285-016-1070-9.pdf application/pdf en http://eprints.nottingham.ac.uk/41032/1/1603.04486.pdf 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 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
repository_type	Digital Repository
institution_category	Local University
institution	University of Nottingham Malaysia Campus
building	Nottingham Research Data Repository
collection	Online Access
language	English English
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.
format	Article
author	Avitable, Daniele Wedgwood, Kyle C. A.
spellingShingle	Avitable, Daniele Wedgwood, Kyle C. A. Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis
author_facet	Avitable, Daniele Wedgwood, Kyle C. A.
author_sort	Avitable, Daniele
title	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_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_sort	macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis
publisher	Springer
publishDate	2017
url	http://eprints.nottingham.ac.uk/41032/ http://eprints.nottingham.ac.uk/41032/ http://eprints.nottingham.ac.uk/41032/ http://eprints.nottingham.ac.uk/41032/8/Coherent%2010.1007_s00285-016-1070-9.pdf http://eprints.nottingham.ac.uk/41032/1/1603.04486.pdf
first_indexed	2018-09-06T13:10:15Z
last_indexed	2018-09-06T13:10:15Z
_version_	1610863781311676416

Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

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