@article{Omel'chenkoLaing2022,
  author    = {Omel'chenko, Oleh and Laing, Carlo R.},
  title     = {Collective states in a ring network of theta neurons},
  series = {Proceedings of the Royal Society of London. Series A, Mathematical, physical and engineering sciences},
  volume    = {478},
  journal   = {Proceedings of the Royal Society of London. Series A, Mathematical, physical and engineering sciences},
  number    = {2259},
  publisher = {Royal Society},
  address   = {London},
  issn      = {1364-5021},
  doi       = {10.1098/rspa.2021.0817},
  pages     = {23},
  year      = {2022},
  abstract  = {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.},
  language  = {en}
}
@article{LaingOmel'chenko2020,
  author    = {Laing, Carlo R. and Omel'chenko, Oleh},
  title     = {Moving bumps in theta neuron networks},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {30},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {4},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5143261},
  pages     = {11},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}