The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro-differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez model to specifically address the role of spherical topology on spatio-temporal pattern generation. We do this using a mixture of Turing instability analysis, symmetric bifurcation theory, centre manifold reduction and direct simulations with a bespoke numerical scheme. In particular we examine standing and travelling wave solutions using normal form computation of primary and secondary bifurcations from a steady state. Interestingly, we observe spatio-temporal patterns which have counterparts seen in the EEG patterns of both epileptic and schizophrenic brain conditions.

用于生成脑电图 (EEG) 信号的 Nunez 模型自然被描述为具有空间相关延迟的球体上的神经场模型。为简单起见，通常在理想化的一维或平面设置中研究该模型的动态实现，无论是阻尼波动方程还是积分微分方程。在这里，我们重新审视原始的 Nunez 模型，专门解决球形拓扑在时空模式生成中的作用。我们结合使用图灵不稳定性分析、对称分岔理论、中心流形约简和采用定制数值方案的直接模拟来实现这一点。特别是，我们使用稳态的一次和二次分岔的范式计算来检查驻波和行波解。有趣的是，我们观察到的时空模式与癫痫和精神分裂症脑部疾病的脑电图模式中的对应物相同。