The European Physical Journal Special Topics

, Volume 223, Issue 13, pp 2979–2988 | Cite as

Periodic solutions to a mean-field model for electrocortical activity

Regular Article Nonlinear Partial Differential Equations
Part of the following topical collections:
  1. Advanced Computational and Experimental Techniques in Nolinear Dynamics. Guest Editors: Elbert E.N. Macau and Carlos L. Pando Lambruschini (Eds.)


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.


Periodic Orbit Hopf Bifurcation European Physical Journal Special Topic Bifurcation Diagram Neutral Stability Curve 
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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.University of Ontario Institute of TechnologyOshawaCanada
  2. 2.INRIA-Nancy Grand Est, team NEUROSYS, Villers-lès-NancyNancyFrance

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