random processes

In this article we compare the characteristics of two types of the intermittent behavior (type­I intermittency in the presence of noise and eyelet intermittency) supposed hitherto to be the different phenomena. We prove that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is proven by the consideration of different sample systems, such as quadratic map, van der Pol oscillator and R ̈ossler system.

The influence of slow processes (random or regular) on the probability distribution of fast random processes is considered. We show that such influence is universal for all random processes, and in some cases this universality is of the multifractal character. As an example we consider stochastic resonance.