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Periodic solutions to a mean-field model for electrocortical activity

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  • Nonlinear Partial Differential Equations
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Abstract

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 motion through an equivariant Hopf bifurcation. We compute part of a family of standing wave solutions, emanating from this point.

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Authors and Affiliations

  1. University of Ontario Institute of Technology, Oshawa, Ontario, Canada

    L. van Veen & K. R. Green

  2. INRIA-Nancy Grand Est, team NEUROSYS, Villers-lès-Nancy, Nancy, France

    K. R. Green

Authors
  1. L. van Veen
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  2. K. R. Green
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Correspondence to L. van Veen.

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van Veen, L., Green, K.R. Periodic solutions to a mean-field model for electrocortical activity. Eur. Phys. J. Spec. Top. 223, 2979–2988 (2014). https://doi.org/10.1140/epjst/e2014-02311-y

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  • DOI: https://doi.org/10.1140/epjst/e2014-02311-y

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