We analyze effects of bounded white and colored noise on nonhyperbolic chaotic attractors in two-dimensional invertible maps. It is shown that first the nonhyperbolic nature is kept even in the presence of strong noise, but secondly already due to weak noise some properties of nonhyperbolic chaos can become similar to those of hyperbolic and almost hyperbolic chaos. We also estimate the stationary probability measure of noisy nonhyperbolic attractors. For this purpose two different methods for calculating the probability density are applied and the obtained results are compared in detail.
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Анищенко et al. (2000) studied this question.
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