Characteristics of Stability Boundary of Nonlinear Continuous Dynamical Systems

Abstract

The theory of differential equations has been widely known and developed in recent years. One of the issues that many authors give their undivided attention to is the stability boundary of nonlinear dynamical systems. In this work, we first review several properties of equilibrium points on the stability boundary. We next extend the characteristics of the stability boundary for a fairly large class of nonlinear dynamical systems. These characteristics are the key to completely determine the stability boundary of nonlinear dynamical systems.