Irregularity of the solutions and Noncompactness of the Global Attracting Set in a Coupled ODE-PDE Model of the Neocortex

CDSNS Colloquium
Monday, November 6, 2017 - 11:15
1 hour (actually 50 minutes)
Skiles 005
Georgia Institute of Technology
We present a mean field model of electroencephalographic activity in the brain, which is composed of a system of coupled ODEs and PDEs. We show the existence and uniqueness of weak and strong solutions of this model and investigate the regularity of the solutions. We establish biophysically plausible semidynamical system frameworks and show that the semigroups of weak and strong solution operators possess bounded absorbing sets. We show that there exist parameter values for which the semidynamical systems do not possess a global attractor due to the lack of the compactness property. In this case, the internal dynamics of the ODE components of the solutions can create asymptotic spatial discontinuities in the solutions, regardless of the smoothness of the initial values and forcing terms.