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We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-I intermittency and random dynamics. We analytically deduce the laws for the distribution of the laminar phases, with the law for the mean length of the laminar phases versus the critical parameter deduced earlier [PRE 62 (2000) 6304] being the corollary fact of the developed theory. We find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations. We discuss also how this mechanism is expected to take place in other relevant physical circumstances.

The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized synchronization is shown to possess a great stability with respect to noise. The reasons of the revealed particularity are explained by means of the modified system approach [A. E. Hramov, A. A. Koronovskii, Phys. Rev. E. 71, 067201 (2005)] and confirmed by the results of numerical calculations and experimental studies. The main results are illustrated using the examples of unidirectionally coupled chaotic oscillators and discrete maps as well as spatially extended dynamical systems. Different types of the model noise are analyzed. Possible applications of the revealed particularity are briefly discussed. PACS. XX.XX.XX No PACS code given practical applications where the level of natural noise is sufficient. The structure of the paper is as follows. Section 1 contains brief description of the generalized synchronization regime, its methods for detection and mechanisms of its arising both in the cases of the absence and presence of noise. The reasons of the stability of the generalized synchronization regime with respect to noise are also discussed in this section. Section 2 presents results of numerical simulation of the influence of noise on the threshold of the synchronous regime arising in several systems with discrete and continuous time as well as spatially extended systems demonstrating spatio-temporal chaos. In Section 3 we describe the experimental setup for the observation of the generalized synchronization regime in the presence of noise in the electronic chaotic circuit and give the results obtained by means of it. Final discussions and remarks are given in Conclusions.

In this Brief Report we study both experimentally and numerically the intermittent behavior taking place near the boundary of the synchronous time scales of chaotic oscillators being in the regime of time scale synchronization. We have shown that the observed type of the intermittent behavior should be classified as the ring intermittency.

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