[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] A new autonomous chaotic system is designed from the Lorenz family of systems and studied its dynamics both theoretically and numerically. Then two such systems are synchronized using a threshold controller as the coupling element by which complete and asynchronization is achieved. The new system is investigated using MATLAB Simulink and Multisim. The results show that based on the control parameter value the system switches from complete to asynchronization. (paper)

[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] Chaos feature criteria tree has many fruits with geometric maps and calculated values. To easily understand how to study chaos identification, we propose one new learning combination solution based on Hilbert transform (HT) and mutual information (MI). The most important coding probe (x-axis) used the HT of locked uniformly distributed random number (LUSRN), so far the y-axis in contrast standard map points to LUDRN. The measure between contrast standard map and unknown map (normalized test data, HT of LUSRN) used MI values. The test cases cover five chaos equations and eighteen quasi-period functions. The results show in statistics that our new maps and corresponding MI values can classify three kinds of signals with periodic, chaotic and random states. And this work may promote rapid growth of an apple embedded in novel chaos criteria. (paper)

[en] The existence of Smale horseshoes in a class of random polynomial maps on the plane is studied. The conditions under which there are invariant sets on which the maps are topologically conjugate with the fullshift on two symbols are obtained. The system is chaotic in the sense of both Li-Yorke and Devaney. The dynamical behavior of the random systems can be described by the product of a probability space and the symbolic space with the two-sided fullshift. (paper)

[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.