Construction of Lyapunov function near bifurcations with application to rotating stall

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 systems near bifurcations. We demonstrate our construction of Lyapunov functions for the Moore-Greitzer model for the rotating stall inception for axial compression systems.