Eur. Phys. J. Special Topics 229, 2215–2224 (2020)
https://doi.org/10.1140/epjst/e2020-900146-9

Regular Article

Forced synchronization of an oscillator with a line of equilibria

¹ Department of Physics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia
² FEMTO-ST Institute/Optics Department, CNRS & University Bourgogne Franche-Comté, 15B avenue des Montboucons, Besançon Cedex 25030, France

^a e-mail: semenov.v.v.ssu@gmail.com

Received: 18 July 2019
Accepted: 8 June 2020
Published online: 28 September 2020

Abstract

The model of a non-autonomous memristor-based oscillator with a line of equilibria is studied. A numerical simulation of the system driven by a periodic force is combined with a theoretical analysis by means of the quasi-harmonic reduction. Both two mechanisms of synchronization are demonstrated: phase and frequency locking and suppression by an external signal. Classification of undamped oscillations in an autonomous system with a line of equilibria as a special kind of self-sustained oscillations is concluded due to the possibility to observe the effect of frequency-phase locking in the same system in the presence of an external influence. It is established that the occurrence of phase locking in the considered system continuously depends both on parameter values and initial conditions. The simultaneous dependence of synchronization area boundaries on the initial conditions and the parameter values is also shown.