What was found
AFTER TAKEOFF, HAD FLUXING VIBRATION ON CLIMB OUT. MONITORED INSTRUMENTS AND NOTHING WAS OUT OF LIMITS. UPON REACHING APPROXIMATELY 18000, NOTICED ATS LEVERS KICKED OFF. FOLLOWED ECAM AND RESET. INFORMED GOC AND MOCC INFLIGHT. NOTICED EGT ON NUMBER TWO ENGINE WAS PULSING TO 800 DEGREES WITH THE RESPECTIVE PEANUT LIGHT ON THE GAUGE BUT NO ECAM. ATS DISENGAGED AGAIN WITH A PULSE TO 1000 DEGREES. LEFT ATS OFF THE REMAINDER OF FLIGHT AND REDUCED THRUST. DECIDED TO RETURN TO MEMPHIS AND INFORMED GOC, UPON TURNING BACK, WE NOTICED THE VIBRATION N1 WOULD GO FROM 0 TO 0.6 WITHOUT A CHANGE IN THROTTLE POSITION. AS A CREW, WE DECLARED AN EMERGENCY TO EXPEDITE GETTING AIRCRAFT ON THE GROUND AND AVOID HIGH THRUST SETTINGS. EMERGENCY DECLARED.