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Waveform transitions have high correlation to spike wave discharges and polyspike wave discharges in seizure dynamics. This research adopts nonlinear dynamics to study the waveform transitions in a cerebral thalamo-coritcal neural network subjected to a square sensory control via discretization and mappings. The continuous non-smooth network outputs are discretized to establish implicit mapping chains or loops for stable and unstable waveform solutions. Bifurcation trees of period-1 to period-2 waveforms as well as independent bifurcation tree of period-3 to period-6 waveforms are obtained theoretically. The independent bifurcation tree should be taken much care during the control since it coexists with global stable waveforms but contains more spikes. Stability and bifurcations of the nonlinear waveform transitions are predicted by eigenvalue analysis of the discretized model. The transient process from unstable waveform to stable waveform is illustrated. The spike adding and period-doubling phenomenon are presented for illustration of the network response after control. The dominant frequency components and the detailed quantity levels of the corresponding amplitudes are exhibited in the harmonic spectrums which can be implemented to controller design for reduction and elimination of the absence seizures. This research presents new perspectives for the waveform transitions and provides theories and data for seizure prediction and regulation. [ABSTRACT FROM AUTHOR]