TY  - JOUR
A1  - Laing, Carlo R.
A1  - Omel'chenko, Oleh
T1  - Moving bumps in theta neuron networks
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We consider large networks of theta neurons on a ring, synaptically coupled with an asymmetric kernel. Such networks support stable "bumps" of activity, which move along the ring if the coupling kernel is asymmetric. We investigate the effects of the kernel asymmetry on the existence, stability, and speed of these moving bumps using continuum equations formally describing infinite networks. Depending on the level of heterogeneity within the network, we find complex sequences of bifurcations as the amount of asymmetry is varied, in strong contrast to the behavior of a classical neural field model.
Y1  - 2020
U6  - https://doi.org/10.1063/1.5143261
SN  - 1054-1500
SN  - 1089-7682
VL  - 30
IS  - 4
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Omel'chenko, Oleh
A1  - Laing, Carlo R.
T1  - Collective states in a ring network of theta neurons
JF  - Proceedings of the Royal Society of London. Series A, Mathematical, physical and engineering sciences
N2  - 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.
KW  - theta neurons
KW  - neural networks
KW  - bumps
Y1  - 2022
U6  - https://doi.org/10.1098/rspa.2021.0817
SN  - 1364-5021
SN  - 1471-2946
VL  - 478
IS  - 2259
PB  - Royal Society
CY  - London
ER  -