Analysis of dynamical robustness of multilayer neuronal networks with inter-layer ephaptic coupling at different scales

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.