The Credible Regions on the Approximate Stability Boundaries of Nonlinear Dynamic Systems

The stability boundary of a nonlinear dynamic system may often be constructed from stable manifolds of type-1 equilibrium points. These stable manifolds are typically approximated numerically, with only local validity. A numerical method is proposed, based on 1- and 2-D characteristic invariant manifolds (CIMs) which lie on the stable manifold and can be computed with greater accuracy than approximations to the entire manifold because of their lower dimension, to estimate credible regions in which the mismatch between the approximate and actual boundaries is below a threshold.