  We consider the behavior of a modulated wave solution to an
$\mathbb{S}^1$-equivariant autonomous system of differential equations under an
external forcing of modulated wave type. The modulation frequency of the
forcing is assumed to be close to the modulation frequency of the modulated
wave solution, while the wave frequency of the forcing is supposed to be far
from that of the modulated wave solution. We describe the domain in the
three-dimensional control parameter space (of frequencies and amplitude of the
forcing) where stable locking of the modulation frequencies of the forcing and
the modulated wave solution occurs.
  Our system is a simplest case scenario for the behavior of self-pulsating
lasers under the influence of external periodically modulated optical signals.
