Periodic solutions in next generation neural field models

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Date
2023-10
DOI
10.1007/s00422-023-00969-6
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Publisher
Springer Nature
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(c) 2023 The Author/s
CC BY 4.0
https://creativecommons.org/licenses/by/4.0/
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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Keywords
Neural field model, Ott/Antonsen, Riccati equation, Self-consistency, Theta neuron, Neural Networks, Computer, Neurons
Citation
Laing CR, Omel'chenko OE. (2023). Periodic solutions in next generation neural field models.. Biol Cybern. 117. 4-5. (pp. 259-274).
URI
https://mro.massey.ac.nz/handle/10179/71395
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