The role of coupling, noise and harmonic impact in oscillatory activity of an excitable FitzHugh–Nagumo oscillator network

Background and Objectives: The dynamics of a separate small ensemble and coupled small ensembles of excitable FitzHugh–Nagumo oscillators is studied. Different topologies and types of coupling between elements, as well as external noise and harmonic impact are considered. Models and Methods: The main model is a ring of five locally coupled excitable FitzHugh–Nagumo neurons, into which additional connections and external disturbances are introduced. Also, two such systems are connected via a hub, represented by a single FitzHugh–Nagumo neuron. To assess the influence of various system parameters on the neuronal spike activity, maps of the average firing frequency are constructed in the plane of control parameters, and the critical values of the parameters necessary for the occurrence of spikes are found. Results: It has been shown that a repulsive local coupling can excite spike activity in a network of excitable oscillators without external impact, and the addition of remote coupling expands the range of parameters in which firings are observed. Besides, by introducing anomalous Lévy noise, it is possible to excite oscillations in the system at lower values of the coupling strength between neurons than by utilising normal Gaussian noise. Also, in a system of two ensembles of neurons connected through a common hub, the interlayer coupling leads not only to synchronisation of the firing frequencies of these ensembles, but also to a transition to the spike activity mode even when no firing was observed in individual ensembles. By changing the parameters of the external harmonic impact and the coupling coefficients of the two ensembles with a common hub, it is possible to influence the average firing frequency.