Computational methods in nonlinear stability analysis: stability boundary calculations

A numerical method is presented for the estimation and the visualization of the stability boundary of an equilibrium point in the state space of autonomous nonlinear dynamical systems. The technique uses a combination of certain concepts from Liapunov theory, numerical simulation and the properties of the geometric structure of the stability boundary. The boundary can be visualized by computing its intersections with arbitrarily selected two-dimensional planes in state space. The visualization problem is reduced to a two-point boundary value differential problem which is solved using a flooding technique.