Based on 2-order Greitzer model of axial flow compressor

a nonlinear analysis of the stall to surge process has been carried out.According to the variation of parameter B

the process was divided into four successive phases

and the compressor system equation was locally linearized.The trend of the system change near the critical point of parameter B was observed and the critical point could be determined accurately.Under the condition that parameter B exceeds its critical value

theorems of Lyapunov stability and local invariable set were introduced to global stability analysis to make up the shortage of local linearization methodology.Compared with numerical simulation

the fact was proved that the compressor system produces stable limit cycle of surge and the system locus converges in finite domain.