Periodic solutions in next generation neural field models

• Published in: Biological cybernetics Vol. 117; no. 4-5; pp. 259 - 274
• Main Authors: Laing, Carlo R., Omel’chenko, Oleh E.
• Format: Journal Article
• Language: English
• 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
• ISSN: 1432-0770; 0340-1200; 1432-0770
• DOI: 10.1007/s00422-023-00969-6

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...