Epilepsy, refractory status epilepticus, and depolarization block are pathological brain activities whose mechanisms are poorly understood. Using a generic mathematical model of seizure activity, we show that these activities coexist under certain conditions spanning the range of possible brain activities. We perform a detailed bifurcation analysis and predict strategies to escape from some of the pathological states. Experimental results using rodent data provide support of the model, highlighting the concept that these pathological activities belong to the endogenous repertoire of brain activities.