Collective dynamics of ensembles of radio engineering models of FitzHugh–Nagumo oscillators coupled via a hub - Ezhov, Dmitry M.; Ponomarenko, Vladimir Ivanovich; Prokhorov, Mikhail Dmitrievich (Известия Саратовского университета. Новая серия Серия: Физика)
Background and Objectives: Since the neural networks of the brain have a multilayer structure, multilayer networks of interconnected model neurons are used to simulate and study their complex dynamics. A central role in establishing and maintaining effective communication between brain regions is played by so-called hubs, which are network nodes connected to many other network nodes. The object of study in this work is a network of model neurons coupled via a hub. We used FitzHugh–Nagumo neurooscillators as node elements of the network. Materials and Methods: The spiking activity of a network consisting of interconnected excitable FitzHugh–Nagumo analog generators was experimentally studied. The collective behavior of elements is considered first in a ring of FitzHugh–Nagumo generators connected by repulsive diffusive couplings, and then in a three-layer network consisting of two such rings connected via a common hub, which is also a FitzHugh–Nagumo generator. Since in a real experimental setup it is impossible to achieve complete identity of analog electronic generators, we numerically studied the effect of weak non-identity of FitzHugh–Nagumo oscillators ontheir collective dynamics and compared the results obtained with experimental ones. The synchronization of analog generators in a three-layer network was studied when the coupling coefficient between the generators of one of the rings and the coupling coefficient between the hub and generators in both rings were varied. Results: Diagrams of the average frequency of spiking activity of generators in each layer of the network have been constructed when the coupling coefficients between the generators of the second ring and between the hub and generators in both rings are varied. It has been shown that in a ring of FitzHugh–Nagumo generators in a radio physical experiment, various oscillatory regimes are observed at fixed values of the parameters of the excitable generators. These regimes differ in the frequency of spikes and the phase shift between the oscillations of various generators in the ring. The existence of switchings between these oscillatory regimes has been revealed. It has been shown that with repulsive couplings of FitzHugh–Nagumo generators inside the rings and repulsive interlayer couplings (connections with the hub), frequency synchronization of all network generators occurs. Conclusion: The obtained results can be used when solving problems of synchronization control in spiking neural networks.