Periodic solutions in next generation neural field models
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...
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| Published in | Biological cybernetics Vol. 117; no. 4-5; pp. 259 - 274 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2023
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1432-0770 0340-1200 1432-0770 |
| DOI | 10.1007/s00422-023-00969-6 |
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| Abstract | 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. |
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| AbstractList | 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. 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.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. |
| Author | Omel’chenko, Oleh E. Laing, Carlo R. |
| Author_xml | – sequence: 1 givenname: Carlo R. orcidid: 0000-0002-6086-2978 surname: Laing fullname: Laing, Carlo R. organization: School of Mathematical and Computational Sciences, Massey University – sequence: 2 givenname: Oleh E. orcidid: 0000-0003-0526-1878 surname: Omel’chenko fullname: Omel’chenko, Oleh E. email: oleh.omelchenko@uni-potsdam.de organization: Institute of Physics and Astronomy, University of Potsdam |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/37535104$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1140_epjp_s13360_025_06072_y crossref_primary_10_1063_5_0244833 crossref_primary_10_1103_PhysRevE_110_064211 crossref_primary_10_1063_5_0205658 crossref_primary_10_1016_j_physa_2025_130416 crossref_primary_10_1103_PhysRevE_110_034411 crossref_primary_10_1103_PhysRevE_111_014422 |
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| Issue | 4-5 |
| Keywords | Ott/Antonsen Riccati equation Neural field model Theta neuron Self-consistency |
| Language | English |
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| Snippet | 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... |
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| SubjectTerms | Bioinformatics Biomedical and Life Sciences Biomedicine Complex Systems Computer Appl. in Life Sciences Cybernetics Neural Networks, Computer Neurobiology Neurons Neurons - physiology Neurosciences Original Original Article Riccati equation |
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| Title | Periodic solutions in next generation neural field models |
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