Effects of coupling memristor noise on synchronization of periodic oscillators

Abstract

This work considers the synchronization of quasi-harmonic Van der Pol oscillators interacting through a memristor with a noise source. White alpha-stable noise (Lévy noise) affects the variable defining the instantaneous state of the memristor, thus causing random fluctuations in the memristive conductance. In the case of a memristor with finite memory, the system exhibits frequency synchronization of the interacting oscillators, independent of the initial state. The cases of Gaussian and non-Gaussian noise of the coupling memristor are considered. In both cases, at low noise levels, the system demonstrates a high degree of effective synchronization in a certain range of frequency detuning and coupling coefficient values. As the noise level increases, the synchronization effect disappears. It is shown that the memristor memory parameter does not affect the steady-state synchronization regime of a deterministic system. However, in the presence of noise in the memristor of coupling, this parameter determines the spectral properties of memristive conductance fluctuations and can control the degree of effective synchronization. The influence of the Lévy noise stability parameter on synchronization is also considered. It is found that for low noise, the effective synchronization improves slightly with decreasing stability parameter.

Speaker

Leonenko Vladislav A.
Saratov State University
Russia

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