Thermal-acoustic instability, which occurs mainly in gas turbine systems of power generation engines and propulsion engines, is accompanied by loud noise and vibration, and in severe cases, damage to the system such as parts destruction and shutdown. Most of the symmetry breaking studies confirmed the phenomenon according to the swirl number and direction in the azimuthal instability, but the symmetry breaking studies in the longitudinal instability are insufficient. In this study, the symmetric breaking phenomenon was investigated by changing the equivalent ratio and arrangement of the swirl number and nozzle to control installation, and the flame mode was defined as an unstable area and a stable area with a phase space reconstruction, 2D FFT, and time signal method. It may be seen that as the symmetry of the swirl number, nozzle arrangement and the equivalent ratio is broken, the instability also decrease.