Modern model-based control theory has led to transformative improvements in our ability to
track the nonlinear dynamics of systems that we observe, and to engineer control systems of …

Seizures can occur spontaneously and in a recurrent manner, which defines epilepsy; or
they can be induced in a normal brain under a variety of conditions in most neuronal …

Mutations in four genes have been identified in familial hemiplegic migraine (FHM), from
which CACNA1A (FHM type 1) and SCN1A (FHM type 3) code for neuronal voltage-gated …

Reliable neural circuit can address the field energy in exact form and equivalent Hamilton
energy is obtained for theoretical models. Furthermore, the energy dependence on firing …

The pathological phenomena of seizures and spreading depression have long been
considered separate physiological events in the brain. By incorporating conservation of …

We developed a neural network model that can account for major elements common to
human focal seizures. These include the tonic-clonic transition, slow advance of clinical …

Cortical activity depends upon a continuous supply of oxygen and other metabolic
resources. Perinatal disruption of oxygen availability is a common clinical scenario in …

Epileptic seizures are characterized by periods of recurrent, highly synchronized activity that
spontaneously terminates, followed by postictal state when neuronal activity is generally …

One characteristic of epilepsy is the variety of mechanisms leading to the epileptic state,
which are still largely unknown. Refractory status epilepticus (RSE) and depolarization block …

In these companion papers, we study how the interrelated dynamics of sodium and
potassium affect the excitability of neurons, the occurrence of seizures, and the stability of …