  We study the effect of noise for a physically realizable flow system with a
hyperbolic chaotic attractor of the Smale - Williams type in the Poincare
cross-section [S.P. Kuznetsov, Phys. Rev. Lett. 95, 2005, 144101]. It is shown
numerically that slightly varying the initial conditions on the attractor one
can obtain a uniform approximation of a noisy orbit by the trajectory of the
system without noise, that is called as the "shadowing" trajectory. We propose
an algorithm for locating the shadowing trajectories in the system under
consideration. Using this algorithm, we show that the mean distance between a
noisy orbit and the approximating one does not depend essentially on the length
of the time interval of observation, but only on the noise intensity. This
dependance is nearly linear in a wide interval of the intensities of noise. It
is found out that for weak noise the Lyapunov exponents do not depend
noticeably on the noise intensity. However, in the case of a strong noise the
largest Lyapunov exponent decreases and even becomes negative indicating the
suppression of chaos by the external noise.
