Periodic solutions in next generation neural field models.
Neural field model
Ott/Antonsen
Riccati equation
Self-consistency
Theta neuron
Journal
Biological cybernetics
ISSN: 1432-0770
Titre abrégé: Biol Cybern
Pays: Germany
ID NLM: 7502533
Informations de publication
Date de publication:
10 2023
10 2023
Historique:
received:
24
01
2023
accepted:
12
07
2023
medline:
26
10
2023
pubmed:
3
8
2023
entrez:
3
8
2023
Statut:
ppublish
Résumé
We 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.
Identifiants
pubmed: 37535104
doi: 10.1007/s00422-023-00969-6
pii: 10.1007/s00422-023-00969-6
pmc: PMC10600056
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
259-274Informations de copyright
© 2023. The Author(s).
Références
Phys Rev E. 2017 Nov;96(5-1):052407
pubmed: 29347806
Neural Comput. 2003 Dec;15(12):2779-822
pubmed: 14629868
PLoS Comput Biol. 2022 May 18;18(5):e1009342
pubmed: 35584147
Phys Rev Lett. 2005 Jun 17;94(23):238103
pubmed: 16090506
Phys Rev E. 2017 Oct;96(4-1):042208
pubmed: 29347589
J Neurosci. 2002 Aug 15;22(16):7297-307
pubmed: 12177225
Front Syst Neurosci. 2021 Feb 10;15:631377
pubmed: 33643004
J Math Neurosci. 2014 Dec;4(1):13
pubmed: 27334377
J Neurosci. 1996 Mar 15;16(6):2112-26
pubmed: 8604055
Phys Rev E. 2021 Aug;104(2):L022203
pubmed: 34525661
Neural Comput. 2005 Mar;17(3):557-608
pubmed: 15802007
Phys Rev Lett. 2009 Jul 24;103(4):044101
pubmed: 19659358
Chaos. 2014 Jun;24(2):023102
pubmed: 24985416
PLoS Comput Biol. 2017 Dec 29;13(12):e1005881
pubmed: 29287081
Chaos. 2008 Sep;18(3):037113
pubmed: 19045487
Nature. 2022 Oct;610(7932):526-531
pubmed: 36224394
Neural Comput. 2001 Jul;13(7):1473-94
pubmed: 11440594
Chaos. 2009 Jun;19(2):023117
pubmed: 19566252
Biol Cybern. 1977 Aug 3;27(2):77-87
pubmed: 911931
Nat Rev Neurosci. 2010 Feb;11(2):100-13
pubmed: 20087360
Front Comput Neurosci. 2020 May 28;14:47
pubmed: 32547379
J Physiol. 2013 Feb 15;591(4):787-97
pubmed: 23184516
Philos Trans A Math Phys Eng Sci. 2019 Sep 9;377(2153):20180121
pubmed: 31329066
Chaos. 2020 Mar;30(3):033133
pubmed: 32237760
Phys Rev E. 2016 Sep;94(3-1):032215
pubmed: 27739712
Nat Neurosci. 2014 Mar;17(3):431-9
pubmed: 24487232
PLoS Comput Biol. 2018 Sep 6;14(9):e1006430
pubmed: 30188889
Phys Rev Lett. 2001 May 7;86(19):4278-81
pubmed: 11328154
PLoS Comput Biol. 2022 Oct 3;18(10):e1010569
pubmed: 36191049
Proc Math Phys Eng Sci. 2022 Mar;478(2259):20210817
pubmed: 35280327
J Neurophysiol. 1989 Feb;61(2):331-49
pubmed: 2918358
Chaos. 2020 Apr;30(4):043117
pubmed: 32357659
J Neurophysiol. 2000 Feb;83(2):808-27
pubmed: 10669496
Phys Rev Lett. 2018 Sep 21;121(12):128301
pubmed: 30296134
Chaos. 2020 Apr;30(4):043103
pubmed: 32357679
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jul;90(1):010901
pubmed: 25122239
Brain Topogr. 2022 Jan;35(1):36-53
pubmed: 33993357
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 2):036213
pubmed: 15089398
Phys Rev E. 2019 Jan;99(1-1):012313
pubmed: 30780315
Philos Trans A Math Phys Eng Sci. 2009 Mar 28;367(1891):1117-29
pubmed: 19218154