Collective states in a ring network of theta neurons | Zendy

Oleh E. Omel’chenko | Zendy; Carlo R. Laing | Zendy

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Collective states in a ring network of theta neurons

Author(s) -

Oleh E. Omel’chenko,

Carlo R. Laing

Publication year - 2022

Publication title -

proceedings of the royal society a 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.

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