Nonlinear dynamics has recently been extensively used to study epilepsy due to the complex nature of the neuronal systems. This study presents a novel method that characterizes the dynamic behavior of pediatric seizure events and introduces a systematic approach to locate the nullclines on the phase space when the governing differential equations are unknown. Nullclines represent the locus of points in the solution space where the components of the velocity vectors are zero. A simulation study over 5 benchmark nonlinear systems with well-known differential equations in three-dimensional exhibits the characterization efficiency and accuracy of the proposed approach that is solely based on the reconstructed solution trajectory. Due to their unique characteristics in the nonlinear dynamics of epilepsy, discriminative features can be extracted based on the nullclines concept. Using a limited training data (only 25% of each EEG record) in order to mimic the real-world clinical practice, the proposed approach achieves 91.15% average sensitivity and 95.16% average specificity over the benchmark CHB-MIT dataset. Together with an elegant computational efficiency, the proposed approach can, therefore, be an automatic and reliable solution for patient-specific seizure detection in long EEG recordings.

中文翻译：

---

使用非线性动力学和零位曲线的特定于患者的癫痫发作检测

由于神经系统的复杂性，非线性动力学最近已广泛用于研究癫痫病。这项研究提出了一种表征小儿癫痫发作动态行为的新颖方法，并介绍了一种在控制微分方程未知时在相空间上定位零线的系统方法。零点线表示解空间中速度矢量的分量为零的点的轨迹。对5个基准非线性系统进行了三维三维仿真研究，结果表明该方法的特征化效率和准确性完全基于重构的求解轨迹，该5个基准非线性系统具有著名的三维微分方程。由于它们在癫痫的非线性动力学中具有独特的特征，可以基于nullclines概念提取判别特征。为了模拟现实世界的临床实践，使用有限的训练数据（每个EEG记录仅占25％），所提出的方法在基准CHB-MIT数据集上实现了91.15％的平均敏感性和95.16％的平均特异性。因此，结合出色的计算效率，所提出的方法可以成为长时间脑电图记录中特定于患者的癫痫发作检测的一种自动且可靠的解决方案。