The pyramidal neuronal population (PY) in the cerebral cortex is closely related to epilepsy, while the excitability of PY is directly affected by the excitatory interneurons (EIN), the inhibitory interneurons (IN), and the thalamic relay nucleus (TC). Based on this, we use the thalamocortical neural field model to explore the dynamic mechanism of system transition by taking the synaptic connection strengths of the above three nuclei on PY as the main factor affecting seizures. The results show that the excitatory effects of EIN on PY induce transitions from 1-spike and wave discharges (SWDs) to 2-spike and wave discharges (2-SWDs), the inhibitory effects of IN on PY induce transitions from saturated state to tonic oscillation state, and the excitatory effects of TC on PY induce transitions from clonic oscillation state to saturated state. According to the single-parameter bifurcation analysis, it is found that Hopf and fold limit cycle bifurcations are the key factors leading to the state transition. In addition, the state analysis of the three pathways is carried out in pairs. The results show that the system produces more types of epileptic seizures with the combined action of EIN and TC on PY. According to the two-parameter bifurcation curve, we obtain the stable parameter areas of tonic-clonic oscillations, SWDs, 2-SWDs and saturated discharges, and clearly find the reasonable transition path between tonic-clonic seizures and absence seizures. This may provide some theoretical guidance for the transmission and evolution of seizures.

In this paper, the transition from anti-phase spike synchronization to in-phase spike synchronization within mixed bursters is investigated in a two-coupled pre-Bözinger complex (pre-BötC) network. In this two-coupled neuronal network, the communication between two pre-BötC networks is based on electrical and synaptic coupling. The results show that the electrical coupling accelerates in-phase spike synchronization within mixed bursters, but synaptic coupling postpones this kind of synchronization. Synaptic coupling promotes anti-phase spike synchronization when electrical coupling is weak. At the same time, the in-phase spike synchronization within dendritic bursters occurs earlier than that within somatic bursters. Asymmetric periodic somatic bursters appear in the transition state from anti-phase spikes to in-phase spikes. We also use fast/slow decomposition and bifurcation analysis to clarify the dynamic mechanism for the two types of synchronization.

An absence seizure is a common neurological disorder primarily associated with abnormal interactions between the corticothalamic network and the basal ganglia. In order to better understand how the basal ganglia contributes to absence seizure regulation, we use an improved mean field model of the basal ganglia-corticothalamo (BGCT) by introducing a direct projection from the glutamatergic mediated subthalamic nucleus to the striatum (STN-D). The results indicate that enhancing the excitatory coupling strength of the STN-D pathway significantly suppresses spike-wave discharges (SWDs) by increasing striatal activation levels, which promotes the transition from the pathological state to either simple oscillations or low firing state. We propose a new stimulation paradigm, namely a four-phase pulse stimulation (FPS), which sequentially delivers four pulses to the striatum (D), thus targeting the cortical excitatory neurons (EPN), specific relay nuclei (SRN), STN, and D. The results indicate that FPS can successfully replace the original inputs to the D and effectively control absence seizures by adjusting the anodal pulse amplitudes ( $A_1$, $A_2$, and $A_3$), which correspond to the excitatory inputs to the D from SRN-D, EPN-D, and SRN-D. These findings offer new insights into understanding the pathophysiology of an absence seizure and its precise therapeutic interventions.