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Dissipative structures are localized, stable patterns that arise due to theintricate balance among dissipation, dispersion, interaction, and externaldrive. Their creation and manipulation are of great interest in fields asdiverse as optics, magnetism, fluids, and the quantum theory. Here, we reporton 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, andcan be varied over a wide range. We show that this system undergoes atransition similar to the prototypical parity-time ($\mathcal{PT}$) symmetrybreaking transition, but in contrast to the usual $\mathcal{PT}$-symmetricmodels, these oscillations are robust against the drive mismatch. By using alossy, nonlinear dimer model with out-of-phase drives, we analytically explainsome of these findings. Our results demonstrate a new way to robustly balancegain and loss in a globally dissipative medium, and manipulate the dissipativestructures.

Rabi oscillations of dissipative structures effected by out-of-phase parametric drives