  Dissipative structures are localized, stable patterns that arise due to the
intricate balance among dissipation, dispersion, interaction, and external
drive. Their creation and manipulation are of great interest in fields as
diverse as optics, magnetism, fluids, and the quantum theory. Here, we report
on the emergence of Rabi oscillations of these patterns in a dissipative,
nonlinear system subject to two localized, out-of-phase, parametric drives.
Their period and amplitude are controlled by the drive size and separation, and
can be varied over a wide range. We show that this system undergoes a
transition similar to the prototypical parity-time ($\mathcal{PT}$) symmetry
breaking transition, but in contrast to the usual $\mathcal{PT}$-symmetric
models, these oscillations are robust against the drive mismatch. By using a
lossy, nonlinear dimer model with out-of-phase drives, we analytically explain
some of these findings. Our results demonstrate a new way to robustly balance
gain and loss in a globally dissipative medium, and manipulate the dissipative
structures.
