Periodic solutions in next generation neural field models

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dc.citation.issue4-5
dc.citation.volume117
dc.contributor.authorLaing CR
dc.contributor.authorOmel'chenko O
dc.coverage.spatialGermany
dc.date.accessioned2024-08-28T03:02:36Z
dc.date.available2024-08-28T03:02:36Z
dc.date.issued2023-10
dc.description.abstractWe consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic solutions. Using the fact that the dynamics at each spatial location are described by a complex-valued Riccati equation we derive a self-consistency equation that such periodic solutions must satisfy. We determine the stability of these solutions, and present numerical results to illustrate the usefulness of this technique. The generality of this approach is demonstrated through its application to several other systems involving delays, two-population architecture and networks of Winfree oscillators
dc.description.confidentialfalse
dc.edition.editionOctober 2023
dc.format.pagination259-274
dc.identifier.author-urlhttps://www.ncbi.nlm.nih.gov/pubmed/37535104
dc.identifier.citationLaing CR, Omel'chenko OE. (2023). Periodic solutions in next generation neural field models.. Biol Cybern. 117. 4-5. (pp. 259-274).
dc.identifier.doi10.1007/s00422-023-00969-6
dc.identifier.eissn1432-0770
dc.identifier.elements-typejournal-article
dc.identifier.issn0340-1200
dc.identifier.pii10.1007/s00422-023-00969-6
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/71395
dc.languageeng
dc.publisherSpringer Nature
dc.publisher.urihttps://link.springer.com/article/10.1007/s00422-023-00969-6
dc.relation.isPartOfBiol Cybern
dc.rights(c) 2023 The Author/s
dc.rightsCC BY 4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectNeural field model
dc.subjectOtt/Antonsen
dc.subjectRiccati equation
dc.subjectSelf-consistency
dc.subjectTheta neuron
dc.subjectNeural Networks, Computer
dc.subjectNeurons
dc.titlePeriodic solutions in next generation neural field models
dc.typeJournal article
pubs.elements-id479263
pubs.organisational-groupOther
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