ABSTRACT
This chapter presents the models of the brain capable of describing epileptic seizures. These are limited to models that are dynamic rather than static, to reflect the time-evolving nature of both the seizures as well as the measured electroencephalogram used to corroborate them. They are also limited to those that reflect the activity of networks rather than single neurons. A stable linear system is incapable of describing oscillations. Transitions into oscillatory behavior in the non-linear system are transitions to instability in a linearized system. Distinguishing between stability and instability is important in the study of epilepsy. The chapter uses the models to help us understand, investigate and infer how seizures are generated and how they can subsequently be terminated. Mathematical model-based epilepsy research studies how parameters in the model can be altered to create seizure-like activity. The meso-scopic model was designed for a normal region of the brain.
