16-86 Farshad Shirani, Wassim M. Haddad, Rafael de la Llave
On the Global Dynamics of an Electroencephalographic Mean Field Model of the Neocortex (2479K, PDF) Oct 11, 16
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Abstract. This paper investigates the global dynamics of a mean field model of the electroencephalogram developed by Liley \emph{et al.}, 2002. The model is presented as a system of coupled ordinary and partial diffe rential equations with periodic boundary conditions. Existence, uniqueness, and regularity of weak and strong solutions of th e model are established in appropriate function spaces, and the associated initi al-boundary value problems are proved to be well-posed. Sufficient conditions are developed for the phase spaces of the model to ensure nonnegativity of certain quantities in the model, as required by their b iophysical interpretation. It is shown that the semigroups of weak and strong solution operators po ssess bounded absorbing sets for the entire range of biophysical values of the p arameters of the model. Challenges towards establishing a global attractor for the model are dis cussed and it is shown that there exist parameter values for which the construct ed semidynamical systems do not posses a compact global attractor, due to the la ck of assymptotic compactness property. Finally, instructive insights provided by the theoretical results of the paper on the computational analysis of the model are discussed.

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