  The stability of the one-mode nonlinear solutions of the Fermi-Pasta-Ulam -
$\beta$ system is numerically investigated. No external perturbation is
considered for the one-mode exact analytical solutions, the only perturbation
being that introduced by computational errors in numerical integration of
motion equations. The threshold energy for the excitation of the other normal
modes and the dynamics of this excitation are studied as a function of the
parameter $\mu$ characterizing the nonlinearity, the energy density $\epsilon$
and the number N of particles of the system. The achieved results confirm in
part previous results, obtained with a linear analysis of the problem of the
stability, and clarify the dynamics by which the one-mode exchanges energy with
the other modes with increasing energy density. In a range of energy density
near the threshold value and for various values of the number of particles N,
the nonlinear one-mode exchanges energy with the other linear modes for a very
short time, immediately recovering all its initial energy. This sort of
recurrence is very similar to Fermi recurrences, even if in the Fermi
recurrences the energy of the initially excited mode changes continuously and
only periodically recovers its initial value. A tentative explanation of this
intermittent behaviour, in terms of Floquet's theorem, is proposed.
