Numerical bifurcation theory for high-dimensional neural models

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dc.citation.issue1
dc.citation.volume4
dc.contributor.authorLaing CR
dc.coverage.spatialGermany
dc.date.available2014-12
dc.date.available2014-06-13
dc.date.issued2014-07-25
dc.description.abstractNumerical bifurcation theory involves finding and then following certain types of solutions of differential equations as parameters are varied, and determining whether they undergo any bifurcations (qualitative changes in behaviour). The primary technique for doing this is numerical continuation, where the solution of interest satisfies a parametrised set of algebraic equations, and branches of solutions are followed as the parameter is varied. An effective way to do this is with pseudo-arclength continuation. We give an introduction to pseudo-arclength continuation and then demonstrate its use in investigating the behaviour of a number of models from the field of computational neuroscience. The models we consider are high dimensional, as they result from the discretisation of neural field models—nonlocal differential equations used to model macroscopic pattern formation in the cortex. We consider both stationary and moving patterns in one spatial dimension, and then translating patterns in two spatial dimensions. A variety of results from the literature are discussed, and a number of extensions of the technique are given.
dc.description.publication-statusPublished
dc.format.extent13 - ?
dc.identifierhttps://www.ncbi.nlm.nih.gov/pubmed/27334377
dc.identifier10.1186/2190-8567-4-13
dc.identifier.citationJ Math Neurosci, 2014, 4 (1), pp. 13 - ?
dc.identifier.doi10.1186/2190-8567-4-13
dc.identifier.elements-id232463
dc.identifier.harvestedMassey_Dark
dc.identifier.issn2190-8567
dc.languageeng
dc.publisherBioMed Central
dc.relation.isPartOfJ Math Neurosci
dc.rights© 2014 C.R. Laing; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.subjectBifurcation
dc.subjectContinuation
dc.subjectNeural field
dc.subjectPseudo-arclength
dc.subject.anzsrc0102 Applied Mathematics
dc.titleNumerical bifurcation theory for high-dimensional neural models
dc.typeJournal article
pubs.notesNot known
pubs.organisational-group/Massey University
pubs.organisational-group/Massey University/College of Sciences
pubs.organisational-group/Massey University/College of Sciences/School of Mathematical and Computational Sciences
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