Peculiarities of the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors in the presence of noise

We study the relaxation to an invariant probability measure on quasihyperbolic and nonhyperbolic chaotic attractors in the presence of noise. We also compare different characteristics of the rate of mixing and show numerically that the rate of mixing for nonhyperbolic chaotic attractors can significantly change under the influence of noise. A mechanism of the noise influence on mixing is presented, which is associated with the dynamics of the instantaneous phase of chaotic trajectories. We also analyze how the synchronization effect can influence the rate of mixing in a system of two coupled chaotic oscillators.