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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Bibliographic Details
Published inBiological cybernetics Vol. 117; no. 4-5; pp. 259 - 274
Main Authors Laing, Carlo R., Omel’chenko, Oleh E.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023
Springer Nature B.V
Subjects
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
Ott/Antonsen
Riccati equation
Neural field model
Theta neuron
Self-consistency
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Summary: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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Communicated by Benjamin Lindner.
ISSN:1432-0770
0340-1200
1432-0770
DOI:10.1007/s00422-023-00969-6