The Stability of Second Order Quadratic Differential Equations

This paper investigates the stability properties of second-order systems, x. = ƒ(x), where ƒ(x) contains either quadratic terms-system (1)-or linear and quadratic terms-system (2)-in x. The principal contributions are summarized in two theorems which give necessary and sufficient conditions for stability and asymptotic stability in the large of systems (1) and (2), respectively.