Equivalence ratio independence and dependence ranges of system responses for a nonlinear thermoacoustic oscillation in a Rijke tube

•The Φ-independence and Φ-dependence range of eigenfrequency is discovered.•Oscillation characteristics and system dynamics conform to the defined ranges.•A stable and less complex system is usually obtained in the Φ-independence range.•Phase difference for harmonic modes is able to analyse oscillation characteristics.•RP and RQA are efficient in analysing nonlinear dynamics of thermoacoustic systems.