ABSTRACT
The advantage of graphical approaches to complex dynamical systems, such as the brain, is that they can be used by neuroscientists to develop interpretations and key experiments even if the underlying mechanisms have not yet been fully identi–ed. We illustrate this approach by showing that mathematical models of neural populations are particularly vulnerable for the production of paroxysmal transient events (possibly seizures) at times when changes in state occur as, for example, the transitions from wakefulness to sleep and through the sleep stages while sleeping. These arguments emphasize the importance of careful studies of the timing of seizure occurrences with respect to sleep stage transitions in patients with nocturnal frontal lobe epilepsy.
