Bifurcation control of a seizing human cortex

Abstract

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.