A system includes a gas turbine engine that includes a first combustor and a second combustor. The first combustor includes a first fuel nozzle disposed in a first head end chamber of the first combustor and a first fuel injector. The first fuel nozzle is configured to inject a first fuel and an oxidant into a first combustion chamber of the first combustor. The second combustor includes a second fuel nozzle disposed in a second head end chamber of the second combustor, a second fuel injector, and a second orifice plate disposed in a second fuel path upstream of the second fuel injector. The second fuel nozzle is configured to inject the first fuel and the oxidant into a second combustion chamber of the second combustor and the second orifice plate is configured to help reduce modal coupling between the first combustor and the second combustor.