  A mathematical model describing the initial stage of the capture into the
parametric autoresonance in nonlinear oscillating systems with a dissipation is
considered. Solutions with unboundedly growing energy in time at infinity are
associated with the autoresonance phenomenon. Stability of such solutions is
investigated. We describe classes of admissible deterministic and random
perturbations such that the stability of autoresonance is preserved on an
asymptotically large interval.
