Eur. Phys. J. Special Topics 223, 2979–2988 (2014)
https://doi.org/10.1140/epjst/e2014-02311-y

Regular Article

Periodic solutions to a mean-field model for electrocortical activity

¹ University of Ontario Institute of Technology, Oshawa, Ontario, Canada
² INRIA-Nancy Grand Est, team NEUROSYS, Villers-lès-Nancy, France

^a e-mail: Lennaert.vanVeen@uoit.ca

Received: 22 July 2014
Revised: 17 October 2014
Published online: 10 December 2014

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.