Open AccessCollective states in a ring network of theta neurons
Author(s) -
Oleh Omel’chenko,
Carlo R. Laing
Publication year - 2022
Publication title -
proceedings - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
eISSN - 1471-2946
pISSN - 1364-5021
DOI - 10.1098/rspa.2021.0817
Subject(s) - bifurcation , homogeneous , ring (chemistry) , stability (learning theory) , mathematics , bifurcation theory , coupling (piping) , state (computer science) , physics , statistical physics , mathematical analysis , computer science , nonlinear system , algorithm , engineering , quantum mechanics , mechanical engineering , chemistry , organic chemistry , machine learning
We consider a ring network of theta neurons with non-local homogeneous coupling. We analyse the corresponding continuum evolution equation, analytically describing all possible steady states and their stability. By considering a number of different parameter sets, we determine the typical bifurcation scenarios of the network, and put on a rigorous footing some previously observed numerical results.