Naima Meskine, NaimaKessal, MohandSeba, Djamila2022-02-172022-02-17202216605446https://link.springer.com/article/10.1007/s00009-021-01933-zDOI 10.1007/s00009-021-01933-zhttps://dspace.univ-boumerdes.dz/handle/123456789/7622Based on the Greitzer’s reduced model, an analytical study on the instabilities phenomena of the operating point is presented using some basic properties of the nonlinear dynamic system. Moreover, a proposal of a general compressor characteristic curve, that suits the stationary system, is given. The Routh–Hurwitz theorem is applied to determine the stability conditions on the model parameters. An analysis along with a discussion is presented when the compression system goes to the Hopf bifurcation point during surge. For the Hopf bifurcation case, an approximate expression, for the periodic cycle of the system’s solution from the equilibrium point, is obtained and the direction is determined using Lyapunov’s stability theory. A numerical simulation is executed to illustrate the theoretical resultsenHopf bifurctionLimit pointSteady stateLocal bifurcationArticle