The present disclosure is directed to a method of operating a combustion system to attenuate combustion dynamics. The method includes flowing, via a compressor section, an overall supply of air to the combustion system; flowing, via a fuel supply system, an overall flow of fuel to the combustion system; flowing, to a first fuel nozzle of the combustion system, a first supply of fuel defining a richer burning fuel-air mixture at the first fuel nozzle; flowing, to a second fuel nozzle of the combustion system, a second supply of fuel defining a leaner burning fuel-air mixture at the second fuel nozzle; and igniting the richer burning fuel-air mixture and the leaner burning fuel-air mixture to produce an overall fuel-air ratio at a combustion chamber of the combustion system.