Purpose. The study focuses on analyzing spike activity and synchronization in ensembles of FitzHugh-Nagumo neurons, both with and without external noise excitation. These networks can induce oscillations at different frequencies, depending on the excitability parameter of individual elements and the coupling strength between them. Additionally, variations in these parameters can lead to synchronization among the elements. The research investigates the dynamics of both a single-layer network, which includes a common element, and a three-layer network with an intermediate neuron-hub layer.

Methods. To analyze the dynamics of the networks under investigation, we calculate the time-averaged spike frequencies of all elements. These frequencies are then averaged for each outer layer and compared with the frequency of the central element, as well as with each other in the case of a multilayer network. In order to assess the impact of coupling strength on the spike activity and synchronization of the network elements, we construct frequency distributions and frequency difference distributions in a plane of coupling strength coefficients.

Results. It has been shown that small single-layer and three-layer networks of identical oscillators (FitzHugh-Nagumo neurons), with a simple coupling topology, can exhibit different spike activity in different parts of the system. In this case, the neurons transition to a self-oscillatory mode due to repulsive coupling between the elements. The research has established that in a single-layer network, a ring of elements can synchronize in frequency with the central element within a specific range of coupling strength values. In a three-layer system, layer synchronization can also be observed. Weak noise has minimal impact on the synchronization boundaries of all three layers, in terms of coupling parameters. However, as the noise intensity increases, this area decreases. At the same time, the noise
leads to the emergence of a new synchronization region in which relay synchronization of the layers is observed in the absence of synchronization with the hub.

Conclusion. The study explored the potential of exciting oscillations and achieving synchronization in single-layer and three-layer networks of coupled FitzHugh-Nagumo oscillators. The coupling strength between the elements varied in order to investigate its impact. Although the study only provided a broad understanding of the spike activity of excitable neurons in the two network models examined, it adequately demonstrated the crucial role of coupling in the spiking activity of these neurons.