In nervous system, a non-synaptic communication between neurons, known as the ephaptic coupling, emerges depending on electromagnetic induction which is induced by extracellular electric fields. In this paper, a multilayer neuronal network is constructed by adopting ephaptic coupling between layers, and dynamical robustness of multilayer neuronal networks with inter-layer ephaptic coupling is analyzed at different scales. The macroscopic oscillation of the whole network occupies the middle ground between mesoscopic oscillation of intermediate layer and that of the top (or bottom) layer. Strong inter-layer ephaptic coupling is capable of suppressing the resonance like phenomena of oscillation at mesoscale and macroscale. At weak electrical coupling, dynamical robustness of intermediate layer is stronger than that of top and bottom layers, and is even stronger than that of the whole network. While at strong electrical coupling, dynamical robustness of each layer is comparable to that of the whole network. The inter-layer ephaptic coupling could enhance dynamical robustness of each layer and the entire multilayer neuronal network, which is in stark contrast to electrical coupling with the tendency to spoil the dynamical robustness. Dynamical robustness of the whole network is always weaker than that of intermediate layer, but is stronger than that of top and bottom layers with increasing inter-layer ephaptic coupling. The firing modes of neurons before the critical ratio is analyzed at microscale. The ratio of inactive neurons switches the firing patterns of the active neuron among different firing patterns in multilayer neuronal network. The dynamics of multilayer neuronal network with inter-layer ephaptic coupling is verified in the analog circuit built on Multisim. This study provides new clues to understand mechanism of collective phenomenon in realistic neuronal systems.

在神经系统中，神经元之间的非突触通讯，称为八触耦合，取决于由细胞外电场引起的电磁感应。本文采用层间耦合构建多层神经元网络，并在不同尺度上分析了具有层间耦合的多层神经元网络的动态鲁棒性。整个网络的宏观振荡处于中间层和顶层（或底层）细观振荡之间的中间地带。强层间表面耦合能够抑制中尺度和宏观尺度上的类似共振的振荡现象。在弱电耦合下，中间层的动态鲁棒性强于顶层和底层，甚至比全网还要强。在强电耦合下，每一层的动态鲁棒性与整个网络的动态鲁棒性相当。层间耦合可以增强每一层和整个多层神经元网络的动态鲁棒性，这与电耦合形成鲜明对比，电耦合倾向于破坏动态鲁棒性。整个网络的动态鲁棒性总是弱于中间层，但随着层间耦合的增加，强于顶层和底层。微尺度分析临界比前神经元的放电模式 层间耦合可以增强每一层和整个多层神经元网络的动态鲁棒性，这与电耦合形成鲜明对比，电耦合倾向于破坏动态鲁棒性。整个网络的动态鲁棒性总是弱于中间层，但随着层间耦合的增加，强于顶层和底层。微尺度分析临界比前神经元的放电模式 层间耦合可以增强每一层和整个多层神经元网络的动态鲁棒性，这与电耦合形成鲜明对比，电耦合倾向于破坏动态鲁棒性。整个网络的动态鲁棒性总是弱于中间层，但随着层间耦合的增加，强于顶层和底层。微尺度分析临界比前神经元的放电模式 但随着层间耦合的增加，比顶层和底层更强。微尺度分析临界比前神经元的放电模式 但随着层间耦合的增加，比顶层和底层更强。微尺度分析临界比前神经元的放电模式. 非活动神经元的比率在多层神经元网络中的不同放电模式之间切换活跃神经元的放电模式。在基于Multisim的模拟电路中验证了具有层间ephaptic耦合的多层神经网络的动力学。这项研究为理解现实神经元系统中集体现象的机制提供了新的线索。