asymptotic stability


asymptotic stability

[ā‚sim′täd·ik stə′bil·əd·ē] (mathematics) The property of a vector differential equation which satisfies the conditions that (1) whenever the magnitude of the initial condition is sufficiently small, small perturbations in the initial condition produce small perturbations in the solution; and (2) there is a domain of attraction such that whenever the initial condition belongs to this domain the solution approaches zero at large times.