Stochastic Motion of Bumps in Planar Neural Fields

@article{Poll2015StochasticMO,
  title={Stochastic Motion of Bumps in Planar Neural Fields},
  author={Daniel B. Poll and Zachary P. Kilpatrick},
  journal={SIAM J. Appl. Math.},
  year={2015},
  volume={75},
  pages={1553-1577}
}
We analyze the effects of spatiotemporal noise on stationary pulse solutions (bumps) in neural field equations on planar domains. Neural fields are integrodifferential equations whose integral kernel describes the strength and polarity of synaptic interactions between neurons at different spatial locations of the network. Fluctuations in neural activity are incorporated by modeling the system as a Langevin equation evolving on a planar domain. Noise causes bumps to wander about the domain in a… 

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