  We propose a neuronal network model which undergoes a saddle-node bifurcation
on an invariant circle as the mechanism of the transition from the interictal
to the ictal (seizure) state. In the vicinity of this transition, the model
captures important dynamical features of both interictal and ictal states. We
study the nature of interictal spikes and early warnings of the transition
predicted by this model. We further demonstrate that recurrent seizures emerge
due to the interaction between two networks.
