Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis

@article{Avitable2016MacroscopicCS,
  title={Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis},
  author={Daniele Avitable and Kyle C. A. Wedgwood},
  journal={Journal of Mathematical Biology},
  year={2016},
  volume={75},
  pages={885 - 928}
}
We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson (Phys Rev E 85(5):055,101(R), 2012), is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of these patterns in various limits using a combination of analytical and numerical techniques. In a purely deterministic version of the model, posed on… 

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