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.

波形转变与癫痫动力学中的尖峰波放电和多尖峰波放电具有高度相关性。本研究采用非线性动力学来研究通过离散化和映射进行方形感觉控制的大脑丘脑皮质神经网络中的波形转变。连续的非光滑网络输出被离散化，以建立隐式映射链或循环，以获得稳定和不稳定的波形解决方案。理论上得到了周期1到周期2波形的分叉树以及周期3到周期6波形的独立分叉树。独立分叉树与全局稳定波形共存，但包含较多尖峰，因此控制时应格外小心。通过离散模型的特征值分析来预测非线性波形转变的稳定性和分岔。图示了从不稳定波形到稳定波形的瞬态过程。提出了尖峰添加和倍周期现象，以说明控制后的网络响应。主频率分量和相应幅度的详细数量水平显示在谐波频谱中，可以将其应用于控制器设计，以减少和消除失神发作。这项研究提出了波形转变的新视角，并为癫痫发作预测和调节提供了理论和数据。