  Nonlinear oscillator systems are ubiquitous in biology and physics, and their
control is a practical problem in many experimental systems. Here we study this
problem in the context of the two models of spatially-coupled oscillators: the
complex Ginzburg-Landau equation (CGLE) and a generalization of the CGLE in
which oscillators are coupled through an external medium (emCGLE). We focus on
external control drives that vary in both space and time. We find that the
spatial distribution of the drive signal controls the frequency ranges over
which oscillators synchronize to the drive and that boundary conditions
strongly influence synchronization to external drives for the CGLE. Our
calculations also show that the emCGLE has a low density regime in which a
broad range of frequencies can be synchronized for low drive amplitudes. We
study the bifurcation structure of these models and find that they are very
similar to results for the driven Kuramoto model, a system with no spatial
structure. We conclude by discussing the implications of our results for
controlling coupled oscillator systems such as the social amoebae
\emph{Dictyostelium} and populations of BZ catalytic particles using spatially
structured external drives.
