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Based 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 results.
Mediterranean Journal of Mathematics – Springer Journals
Published: Feb 1, 2022
Keywords: Hopf bifurction; limit point; steady state; local bifurcation; axial compressor; Primary 34C23; Secondary 34D20
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