  We study the dynamics of an ensemble of non-interacting harmonic oscillators
in a nonlinear dissipative environment described by the Nos\'e - Hoover model.
Using numerical simulation we find the histogram for total energy, which agrees
with the analysis of the Nos\'e - Hoover equations effected with the method of
averaging. The histogram does not correspond to Gibbs' canonical distribution.
We have found oscillations at frequency proportional to $\sqrt{\alpha/m}$,
$\alpha$ the dissipative parameter of thermostat and $m$ the characteristic
mass of particle, about the stationary state corresponding to equilibrium. The
oscillations could have an important bearing upon the analysis of simulating
molecular dynamics in the Nos\'e - Hoover thermostat.
