ISSN 1063-7842, Technical Physics, 2011, Vol. 56, No. 7, pp. 909–913. © Pleiades Publishing, Ltd., 2011. Original Russian Text © M.O. Zhuravlev, A.A. Koronovskii, O.I. Moskalenko, A.E. Hramov, 2011, published in Zhurnal Tekhnicheskoі Fiziki, 2011, Vol. 81, No. 7, pp. 7–12. 909 INTRODUCTION Synchronization of random oscillations is one of the fundamental phenomena observed in a wide class of objects in nature and engineering, which arises keen interest of researchers [1, 2]. The interest in this phe- nomenon is due to its considerable theoretical impor- tance [1] as well as a wide range of practical applica- tions (e.g., covert data transmission [3, 4], biological, chemical, and physical problems [5], and control of chaos, including in microwave electronic systems [6, 7]). Several types of synchronous behavior of one-way mutually coupled dynamic systems (such as phase locking [8], generalized synchronization [9], lag syn- chronization [10], complete synchronization [11], and time scale synchronization [12]) have been revealed; each of these types is characterized by its own specific features and diagnostic methods. Analysis of states preceding synchronization is of special interest in the study of synchronous dynamics of chaotic systems. It has been established in numer- ous publications in this field (see, for example, [13]) that a transition from synchronous to asynchronous regime is performed as a rule via intermittent behavior observed near the synchronization boundary [10, 14]. In addition, it is well known that each synchronization type is preceded by its own type of intermittence. Intermittence is an important phenomenon observed in nonlinear systems (in particular, it is one of univer- sal scenarios of the transition from a periodic to cha- otic motion [15, 16]). A certain classification of inter- mittent behavior exists; in particular, we can single out type I–III intermittency [5, 7], on–off intermittency [18–20], “needle’s eye” intermittency [21], ring inter- mittency [13], etc. All these types of intermittency are observed in various physical and biological systems [10, 22]. From the known types of synchronous behavior, time scale synchronization is of special interest [12]. This type of synchronous chaotic dynamics makes it possible to consider all above-mentioned types of cha- otic synchronization from unified positions. More- over, it can be diagnosed even when detection of other types of synchronous behavior is problematic (e.g., diagnosing of chaotic phase locking in the case of phase-incoherent attractor [23]), which makes it wide-spread and important for various applications. It is also important to note rich potentialities of chaotic synchronization diagnostics using the time scale syn- chronization method in the case of multiscale chaos. Time scale synchronization is based on analysis of the behavior of the systems in question on different time scales introduced by a continuous wavelet trans- formation with a complex basis [24]. In this case, the regime is referred to as a time scale synchronization if for temporal implementations generated by the system considered here, there exists a range of time scales for which synchronous behavior is observed [12]. Analysis of the intermittent behavior at the synchronization bound- ary of time scales is of considerable interest because the knowledge of these effects can provide a better under- standing of the mechanisms of stabilization of this type of chaotic synchronization in coupled systems. We will consider the behavior of one-way coupled Ressler systems at the boundary between synchronous and asynchronous time scales. 1 Upon a change in the observation scale, the observed behavior changes in this case from synchronous to asynchronous, or vice versa. The technique for determining the durations of laminar and turbulent phases in the given case was worked out, tested, and described in [25]. Here, we consider the regularities governing such a change in the behavior, which gives an idea about the mecha- 1 In the synchronous time scale mode (for a fixed set of control parameters) both synchronous and asynchronous dynamics can be observed for different time scales of observation [12]. Intermittent Behavior at the Time Scale Synchronization Boundary M. O. Zhuravlev, A. A. Koronovskii, O. I. Moskalenko, and A. E. Hramov Saratov State University, Astrakhanskaya ul. 83, Saratov, 410012 Russia e-mail: pifos@bk.ru Received May 12, 2010; in final form, October 8, 2010 Abstract—The intermittent behavior observed at the time scale synchronization boundary of interacting ran- dom oscillators operating in time scale synchronization mode is analyzed. Analysis of statistical characteris- tics (distributions of laminar segment lengths and the dependence of the average laminar segment length on the supercriticality parameter) shows that the observed intermittent behavior is ring intermittency. DOI: 10.1134/S1063784211070267 THEORETICAL AND MATHEMATICAL PHYSICS