A system with a gas turbine engine is provided. The gas turbine engine includes a first combustor comprising a first fuel nozzle, a second combustor comprising a second fuel nozzle, and a first fuel pressure oscillation system. The first fuel pressure oscillation system includes a first rotary device coupled to a first fuel circuit. The first fuel circuit is disposed along a first fuel passage leading to the first fuel nozzle. The first rotary device is configured to generate a first fuel pressure oscillation through the first fuel nozzle. The gas turbine engine also includes a second fuel pressure oscillation system having a second rotary device coupled to a second fuel circuit. The second fuel circuit is disposed along a second fuel passage leading to the second fuel nozzle, and the second rotary device is configured to generate a second fuel pressure oscillation through the second fuel nozzle.