  We present a study of three-mode parametric instability in large-scale
gravitational-wave detectors. Previous work used a linearised model to study
the onset of instability. This paper presents a non-linear study of this
phenomenon, which shows that the initial stage of exponential rise of the
amplitudes of a higher order optical mode and the mechanical internal mode of
the mirror is followed by a saturation phase, in which all three participating
modes reach a new equilibrium state with constant oscillation amplitudes.
Results suggest that stable operation of interferometers may be possible in the
presence of such instabilities, thereby simplifying the task of suppression.
