An equilibrium of a dynamical system is Lyapunov stable if any suitably small perturbation from the equilibrium results in the system staying near the equilibrium forever. More precisely, given a metric d on the phase space, an equilibrium e is Lyapunov stable if for all ε‎ > 0 there exists δ‎ > 0 so that if d(x(0),e) < δ‎, then d(x(t),e) < ε‎ for all t, where x(t) denotes the evolution of the system following the perturbation. Further, the equilibrium is said to be asymptotically stable if x(t) → e as t→∞ if d(x(0),e) < δ‎.