A gas turbine engine combustor includes: a head end section containing a fuel nozzle assembly and defining a head end air plenum; and a liner extending downstream from the head end section toward an aft frame and defining a combustion chamber therein. First injectors are disposed at a first axial location spaced apart from the head end section to direct a first fuel/air mixture through the liner. A dynamics mitigation system includes cold-side resonators disposed wholly within the head end air plenum, each resonator of the plurality of cold-side resonators having a resonator body with a closed end and an open neck extending from the resonator body opposite the closed end. Each resonator body defines a respective volume, and the open neck is in fluid communication with the head end air plenum. In some embodiments, quarter-wave tube dampers are installed within the fuel nozzle assembly of the head end section.