Influence of colored noise on chaotic systems

We focus on classical chaotic systems corrupted by white and colored noise. We study the dependence of the correlation dimension and the Kolmogorov entropy on the noise level and its spectral exponent. As is well known, white noise strongly reduces the width of the scaling region for the correlation dimension and entropy. On the contrary, we demonstrate that colored noise does not basically obscure the scaling region, changing only the shape of the correlation sum for length scales smaller than the noise level. The numerical results show that, even for a noise level as high as similar to5%, a reasonably wide plateau for the correlation sum is still obtained, but the value of the calculated dimension is somewhat increased. The calculated correlation dimension is a bilinear function of the noise level and the dimension of the noise, which depends on the spectral exponent of the noise. On the other hand, the width of the scaling region for the correlation entropy depends on this spectral exponent, but the value of the plateau does not change substantially.