Visser S, Nicks R, Faugeras O, Coombes S
School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK.
Wellcome Trust Centre for Biomedical Modelling and Analysis, RILD Building, University of Exeter, EX2 5DW, UK.
Physica D. 2017 Jun 15;349:27-45. doi: 10.1016/j.physd.2017.02.017.
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）信号的努涅埃斯模型自然地被描述为具有空间相关延迟的球面上的神经场模型。为了简单起见，该模型的动力学实现形式，无论是作为阻尼波动方程还是积分 - 微分方程，通常都是在理想化的一维或平面设置中进行研究的。在这里，我们重新审视原始的努涅斯模型，以专门探讨球面拓扑结构在时空模式生成中的作用。我们通过结合图灵不稳定性分析、对称分岔理论、中心流形约化以及使用定制数值方案进行直接模拟来实现这一点。特别是，我们使用从稳态出发的一次和二次分岔的范式计算来研究驻波和行波解。有趣的是，我们观察到了在癫痫和精神分裂症脑部疾病的脑电图模式中出现的对应时空模式。
