Bifurcation control of a seizing human cortex.
We consider as a mathematical model of human cortical electrical activity a system of fourteen ordinary differential equations. With appropriate parameters, the model produces activity characteristic of a seizure. To prevent such seizures, we incorporate feedback controllers into the model dynamics. We show that three controllers--a linear feedback controller, a differential controller, and a filter controller--can be used to eliminate seizing activity in the model system. We show how bifurcations induced by the linear controller alter those present in the original dynamics.
Kramer
Mark A
MA
Program in Applied Science and Technology, University of California, Berkeley, CA 94720, USA.
Lopour
Beth A
BA
Kirsch
Heidi E
HE
Szeri
Andrew J
AJ
D000200:Action Potentials; D001683:Biological Clocks; D002540:Cerebral Cortex / Q000503:physiopathology*; D003198:Computer Simulation; D004569:Electroencephalography / Q000379:methods*; D005246:Feedback; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000503:physiopathology*; D009474:Neurons; D012640:Seizures / Q000503:physiopathology*