Synchronization of traveling waves in a two-layer network of FitzHugh-Nagumo excitable neurons with a noisy intensity of interlayer interaction
Ibadulla R. Ramazanov1, Ivan A. Korneev1, Andrei V. Slepnev1, Tatiana E. Vadivasova1
1Saratov State University, Saratov, Russia
Abstract
The effects of synchronization of wave propagating in two layers of a network of excitable FitzHugh-Nagumo oscillators with ring topology are considered. The intralayer coupling of oscillators is assumed to be local and dissipative, while the coupling between layers is stochastic. The strength of the pairwise interaction of oscillators belonging to different layers is set by independent sources of color Gaussian noise with zero mean value. A numerical study of the system of stochastic differential equations describing this model of a network made it possible to reveal the effects of synchronization of excitation waves propagating in two layers. It is shown that in the case of identical layers, with a given phase shift of traveling waves in the absence of interlayer links, noisy coupling with certain characteristics makes it possible to obtain a regime close to complete (in-phase) synchronization of traveling waves. In a network with non-identical layers, in which excitation waves propagate at different speeds and, accordingly, the frequencies of oscillations in time are different, the introduction of a noisy coupling between the layers leads to synchronization of the wave propagation velocities and average oscillation frequencies. Dependences of the average synchronization error (average over time and ensemble of oscillators of the squared deviation of instantaneous states) and also the ratio of the average periods of oscillations (for the case of non-identical layers) on the intensity of noise interaction are constructed for the noise sources with different spectral-correlation properties. The existence of an optimal width of the color noise spectrum for achieving synchronization has been established.
Thus, it was shown that the effects of synchronization of phases and propagation velocities of excitation waves in two-layer network of excitable oscillators can be controlled using random interaction processes given by statistically independent zero-mean noise sources. In this case, both the noise intensity and its correlation time can serve as control parameters.
Speaker
Tatiana Vadivasova
Saratov Stata University
Russia
Discussion
Ask question
