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The inception to rotating stall in axial compressors with inlet distortions is theoretically investigated by studying the three state Moore-Greitzer model with periodic perturbations. The model is transformed into a normal form by using the center manifold theory. Based on the normal form, we derived analytically the periodic solutions as well as their stability boundaries. When the amplitudes of...
We explicitly construct Lyapunov functions for nonlinear systems near two types of bifurcations, namely the equilibrium bifurcations and the Hopf bifurcations. The construction relies on linear and nonlinear coordinate transformation of local center manifold and normal form. The Lyapunov functions are expected to be useful for stability and performance analysis on the effects of noises for nonlinear...
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