Periodic solutions to a mean-field model for electrocortical activity

@article{Veen2014PeriodicST,
  title={Periodic solutions to a mean-field model for electrocortical activity},
  author={Lennaert van Veen and Kevin R. Green},
  journal={The European Physical Journal Special Topics},
  year={2014},
  volume={223},
  pages={2979-2988}
}
We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic inputs. The coupling of these components is represented by sigmoidal and quadratic nonlinearities. We consider these equations on a square domain with periodic boundary conditions, in the vicinity of the primary transition from a stable equilibrium to time-periodic… 
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References

SHOWING 1-10 OF 28 REFERENCES
A spatially continuous mean field theory of electrocortical activity
TLDR
The results suggest that the classically described alpha may be instantiated in a number of qualitatively distinct dynamical regimes, all of which depend on the integrity of inhibitory-inhibitory population interactions.
Travelling waves in models of neural tissue: from localised structures to periodic waves
We consider travelling waves (fronts, pulses and periodics) in spatially extended one dimensional neural field models. We demonstrate for an excitatory field with linear adaptation that, in addition
Spatiotemporal dynamics of continuum neural fields
TLDR
This work surveys recent analytical approaches to studying the spatiotemporal dynamics of continuum neural fields, an important example of spatially extended excitable systems with nonlocal interactions.
A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
TLDR
It is shown that this particular mode reproduces some of the phenomenology of visual psychophysics, including spatial modulation transfer function determinations, certain metacontrast effects, and the spatial hysteresis phenomenon found in stereopsis.
On conductance-based neural field models
TLDR
A conductance-based neural field model that combines biologically realistic synaptic dynamics—based on transmembrane currents—with neural field equations, describing the propagation of spikes over the cortical surface is introduced.
Large-scale model of mammalian thalamocortical systems
TLDR
The model exhibits behavioral regimes of normal brain activity that were not explicitly built-in but emerged spontaneously as the result of interactions among anatomical and dynamic processes, including spontaneous activity, sensitivity to changes in individual neurons, emergence of waves and rhythms, and functional connectivity on different scales.
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