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Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points

A dynamical characterization of the stability boundary for a fairly largeclass of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddlenode equilibrium points on the stability boundary. The stability boundary of anasymptotically stable equilibrium point is shown to consist of the stable manifoldsof the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.