Starting from the typical dynamic characteristics of the complete rotating stall process of low-speed axial compressor

such as catastrophe and hysteresis

by comparing and analyzing the topological properties

the rotating stall and cusp catastrophic model of catastrophe theory were proved similar in spatial topology; then

based on the topological invariance theorem through developing the effective topological mapping method

the topological mapping relationship of the catastrophe point set between the rotating stall and the cusp catastrophic model was established. The applied effect of the model in two low-speed axial compressors showed that cusp catastrophic model can qualitatively describe the catastrophe

hysteresis and bifurcation of the complete rotating stall process of low-speed compressor with the characteristic of “abrupt stall” under different speed conditions; through the mapping method developed

the stall points and recovery points obtained by experiment can be entirely mapped to the model line

which means the cusp catastrophic model can accurately describe the instability boundary of rotating stall.