Stochastic resonance and synchronization in excitable oscillators

Author: Tamar Nikvashvili
Co-authors: Tamar Nikvashvili, Mariam Tsindeliani
Keywords: excitable oscillators, stochastic resonance, FitzHugh-Nagumo, neurons, synchronization, external forces, harmonic effects, noise.
Annotation:

In the report, we discuss the Fitzhugh-Nagumo model of an excitable oscillator for a single neuron. The oscillator starts a high-amplitude oscillations for the threshold value of the external influence. In research, we use harmonic and random external influences. By selecting the parameters, the effect of stochastic resonance is obtained, when the action of an external random force amplifies the influence of the harmonic force. The next step was to investigate a system consisting of two linked, interconnected neurons. Synchronization effect is obtained through numerical experiments. Finally, we got the optimal dependence on the magnitude of the bond coefficient. It is shown that synchronization is obtained for a certain value of the bond coefficient. In the same model, in the case of two coupled neurons, the effect of stochastic resonance is achieved, when noise affects one oscillator and the harmonic affects the other. We present a well-known hypothesis, according to which epilepsy is the result of synchronization of the central nervous system.