The nonlinear bifurcation behavior of two self-excited interacting swirl flames was investigated in a model lean-premixed gas turbine combustor. We examined the system’s thermoacoustic state using several time series analysis methods, including spectrograms, phase portraits, and recurrence plots. It was shown that the state of the system in response to the variation of the combustor length is influenced by the presence of multiple attractors, eventually leading to an extremely large amplitude limit cycle via a subcritical bifurcation.