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We study the effect of noise for a physically realizable flow system with ahyperbolic chaotic attractor of the Smale - Williams type in the Poincarecross-section [S.P. Kuznetsov, Phys. Rev. Lett. 95, 2005, 144101]. It is shownnumerically that slightly varying the initial conditions on the attractor onecan obtain a uniform approximation of a noisy orbit by the trajectory of thesystem without noise, that is called as the "shadowing" trajectory. We proposean algorithm for locating the shadowing trajectories in the system underconsideration. Using this algorithm, we show that the mean distance between anoisy orbit and the approximating one does not depend essentially on the lengthof the time interval of observation, but only on the noise intensity. Thisdependance is nearly linear in a wide interval of the intensities of noise. Itis found out that for weak noise the Lyapunov exponents do not dependnoticeably on the noise intensity. However, in the case of a strong noise thelargest Lyapunov exponent decreases and even becomes negative indicating thesuppression of chaos by the external noise.

The effect of noise on a hyperbolic strange attractor in the system of two coupled van der Pol oscillators