[en] There are various definitions of chaotic dynamical systems. The most utilized definition of chaos is Devaney chaos which isolates three components as being the essential features of chaos; transitivity, dense periodic points and sensitive dependence on initial conditions. In this paper, we focus on a strong dense periodicity property i.e. the set of points with prime period at least n is dense for each n. On shift of finite type over two symbols Σ_2, we show that the strong dense periodicity property implies another strong chaotic notions; locally everywhere onto (also called exact) and totally transitive

[en] This paper discusses the chaotic pseudo-random number generator (CPRNG), which is used in block cipher mode of operation called PM-DC-LM. PM-DC-LM is one of possible subversions of general PM mode. In this paper is not discussed the design of PM-DC-LM, but only CPRNG as a part of it because designing is written in other papers. Possibilities, how to change or to improve CPRNG are mentioned. The final part is devoted for a little testing of CPRNG and some testing data are shown.

[en] Slow Slip Events (SSEs) are episodic slip events that play a significant role in the moment budget along a subduction megathrust. They share many similarities with regular earthquakes, and have been observed in major subduction regions like, for example, Cascadia, Japan, Mexico, New Zealand. They show striking regularity, suggesting that it might be possible to forecast their size and timing, but the prediction of their extension and exact timing is still yet to come.

[en] Development and introduction of nanotechnologies in the oil industry is one of the most pressing issues of the present times.For the first time in the world practice scientific-methodological basis and application practice of nanotechnologies in oil industry is developed on the basis of uniform, scientifically proven approach by taking into account the specificities of oil and gas industry.The application system of such nanotechnologies was developed in oil and gas production.Mathematical models of nanotechnological processes, i.e.^chaos regulation^and hyper-accidental process were offered. Nanomedium and nanoimpact on the ^well-layer^system was studied. Wide application results of nanotechnologies in SOCAR's production fields in oil and gas production are shown.Research results of ^NANOSAA^on the basis of ^NANO + NANO^effect are described in the development.For the first time in world practice ^NANOOIL^,NANOBITUMEN^,NANOGUDRON' and ^NANOMAY' systems on the basis of machine waste oil in the drilling mud were developed for the application in oil and gas drilling. Original property, ^effect of super small concentrations^and ⁿanomemoryⁱn ^NANOOIL^and ^NANOBITUMEN^systems was discovered.By applying ^NANOOIL^,NANOBITUMEN^and ^NANOMAY^systems in the drilling process was discovered: the increase of linear speed, early turbulence, decrease of hydraulic resistance coefficient and economy in energy consumption.Hyper-accidental evaluation of mathematical expectation of general sum of values of the surface strain on the sample data is spelled out with the various experiment conditions. Estimated hyper-accidental value of the mathematical expectation allows us to offer practical recommendations for the development of new nanotechnologies on the basis of rheological parameters of oil.

[en] We follow Stanislavsky's approach of Hamiltonian formalism for fractional systems, as a model problem for the study of chaotic Hamiltonian systems. We prove that his formalism can be retrieved from the fractional embedding theory. We deduce that the fractional Hamiltonian systems of Stanislavsky stem from a particular least action principle, said to be causal. In this case, the fractional embedding becomes coherent.

[en] In the last years, chaotic systems have been applied in information security. These systems have a complex and unpredictable behavior, what makes them more attractive for data cryptography applications. In this work, the chaotic behavior of signals generated by Chua's system is combined with the original information in order to obtain a safe cryptographic method. The experimental results demonstrate that the proposed scheme can be used in data cryptography applications.

[en] We generate multi-mode nonclassical correlations in the output field from the single-mode nonclassicality in the input field with a unitary optical device. It is shown that, according to the invariance of nonclassicality, the decrement of the single-mode nonclassicality is compensated for by the appearance of multi-mode nonclassical correlations. We demonstrate a complete transfer of single-mode nonclassicality to a multi-mode nonclassical correlation for a 1 × 2 array of beam splitters, when chaotic lights are taken as auxiliary classical fields of the input.

[en] The study of complex networks enables us to understand the collective behavior of the interconnected elements and provides vast real time applications from biology to laser dynamics. In this paper, synchronization of complex network of chaotic systems has been studied. Every identical node in the complex network is assumed to be in Lur’e system form. In particular, delayed coupling has been assumed along with identical sector bounded nonlinear systems which are interconnected over network topology

[en] The gyrokinetic description of particle dynamics faces a basic difficulty when a special type of canonical variables is sought, i.e., the so-called gyrokinetic canonical variables. These are defined in such a way that two of them are respectively identified with the gyrophase-angle, describing the fast particle gyration motion around magnetic field lines, and its canonically conjugate momentum. In this paper we intend to discuss the conditions of existence for these variables.

[en] We consider a general coupling of two chaotic dynamical systems and we obtain conditions that provide delayed synchronization. We consider four different couplings that satisfy those conditions. We define Window of Delayed Synchronization and we obtain it analytically. We use four different free chaotic dynamics in order to observe numerically the analytically predicted windows for the considered couplings. (paper)