Stability of bumps in piecewise smooth neural fields with nonlinear adaptation

@inproceedings{Kilpatrick2010StabilityOB,
  title={Stability of bumps in piecewise smooth neural fields with nonlinear adaptation},
  author={Zachary P. Kilpatrick and Paul C. Bressloff},
  year={2010}
}
We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synapticweights between populations of neuronswhosemean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation… CONTINUE READING

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