  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
periodical force is combined with a theoretical analysis by means of the
quasi-harmonic reduction. Both two mechanisms of synchronization are
demonstrated: capture of the phase and frequency of oscillations 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.
