A quantitative analysis of the dynamics of generalized epileptic seizures is carried out by using a neural field model of the corticothalamic system in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. The temporal and dynamical characteristics of generalized absence seizure and tonic-clonic seizures and the interictal oscillations in between two successive seizures are analyzed and related to the corresponding physiological changes of the connection strength. It is found that the spectral, temporal, and physiological characteristics of seizure oscillations changes with the rate of change and amplitude of the connection strength, including appearance of a saddle-cycle at high ramp rates in the tonic-clonic case. The transitions between different states during seizures are inversely proportional to the square root of the ramp rate. The amplitude and sharpness of the interictal oscillations increase with the maximum connection strength, and the number of oscillations only depends on the duration above the threshold.