Effects of strong noise on attractors of dynamical systems

Stationary solutions of the Fokker-Planck equation are found by expansions of the probability distribution with respect to the reciprocal noise strength. It is shown that this expansion is convergent. Explicit representations for the probability distribution are obtained by numerical simulations for the Lorenz model and for a model of generators with inertial nonlinearity (GIN). The obtained distributions show an increasing amount of fine structure with decreasing noise which more and more reflects the fractal attractor structure. Results of measurements of the power spectrum of the GIN and of the distribution in the phase space are presented in dependence on the noise strengths.     

Statistical characteristics of the Poincaré return times for a one-dimensional nonhyperbolic map

Characteristics of the Poincaré return times are considered in a one-dimensional cubic map with a chaotic nonhyperbolic attractor. Two approaches, local one (Kac’s theorem) and global one related with the AP-dimension estimation of return times, are used. The return times characteristics are studied in the presence of external noise. The characteristics of Poincaré recurrences are compared with the form of probability measure and the complete correspondence of the obtained results with the mathematical theory is shown. The influence of the attractor crisis on the return time characteristics is also analyzed. The obtained results have a methodical and educational significance and can be used for solving a number of applied tasks.     

DFT calculation and assignment of vibrational spectra of aryl and alkyl chlorophosphates

DFT calculations of vibrational spectra of chlorophosphates using wide range of basis sets and hybrid functionals were performed. Good agreement between calculated and experimental vibrational spectra was reached by the combination of non-empirical functional PBE0 with both middle and large basis sets. The frequencies of the stretching vibrations of the phosphate group calculated using semi-empirical functional B3LYP for all basis sets deviate significantly from the experimental values. The number of polarization functions on heavy atoms was shown to be a key factor for the calculation of vibrational frequencies of organophosphates. The importance of consideration of all the stable rotamers for a complete assignment of fundamental modes was shown.      

Reactions of C-phosphorylated acetimidates and acetamidines,involving the CH-acid methylene group

Organophosphorus compounds are widely used in the synthesis of pharmaceuticals, fungicides, pesticides, and other biologically active compounds. The review presents the main methods of synthesis of C-phosphorylated acetimidates and acetamidines containing a CH-acid methylene group, as well as reactions involving this group.     

p-Tyrosol: a new synthetic method and new types of pharmacological activity

Russian Chemical Bulletin - A new method for the synthesis of p-tyrosol, i.e., 2-(4-hydroxyphenyl)ethanol, has been developed, which considerably simplified the process of preparation of this...     

Discovery of novel promising targets for anti-AIDS drug developments by computer modeling: application to the HIV-1 gp120 V3 loop

The V3 loop on gp120 from HIV-1 is a focus of many research groups involved in anti-AIDS drug studies, because this region of the protein determines the preference of the virus for T-lymphocytes or primary macrophages. Although the V3 loop governs cell tropism and, for this reason, exhibits one of the most attractive targets for anti-HIV-1 drug developments, its high sequence variability is a major complicating factor. Nevertheless, the data on the spatial arrangement of V3 obtained here for different HIV-1 subtypes by computer modeling clearly show that, despite a wide range of 3D folds, this functionally important site of gp120 forms at least three structurally invariant segments, which contain residues critical for cell tropism. It is evident that these conserved V3 segments represent potential HIV-1 vulnerable spots and, therefore, provide a blueprint for the design of novel, potent and broad antiviral agents able to stop the HIV's spread.     

Stochastic self-sustained oscillations of non-autonomous systems

In the present minireview, we analyze autonomous and non-autonomous oscillations of dynamical and stochastic systems in the framework of common concepts. We introduce the definition of an attractor for a non-autonomous system. We also propose the definition of self-sustained oscillations, which can be applied for both autonomous and non-autonomous systems. We consider noise-induced oscillations and formulate the definition of stochastic self-sustained oscillations for this case. All the statements made in this work are illustrated by particular examples.     

Fluctuational escape from a quasi-hyperbolic attractor in the Lorenz system

Noise-induced escape from the basin of attraction of a quasi-hyperbolic chaotic attractor in the Lorenz system is considered. The investigation is carried out in terms of the theory of large fluctuations by experimentally analyzing the escape prehistory. The optimal escape trajectory is shown to be unique and determined by the saddle-point manifolds of the Lorenz system. We established that the escape process consists of three stages and that noise plays a fundamentally different role at each of these stages. The dynamics of fluctuational escape from a quasi-hyperbolic attractor is shown to differ fundamentally from the dynamics of escape from a nonhyperbolic attractor considered previously [1]. We discuss the possibility of analytically describing large noise-induced deviations from a quasi-hyperbolic chaotic attractor and outline the range of outstanding problems in this field.     

Diagnostics of stochastic resonance using Poincaré recurrence time distribution

In the paper we calculate the distribution density of Poincaré recurrence times for a one-dimensional nonhyperbolic cubic map subjected to white noise and a harmonic signal. It is established that for small vicinities of recurrence the distribution density is not described by an exponential law and is periodically modulated with the external signal frequency. It is shown that the Fourier spectrum of the distribution density exhibits a well-distinguishable peak at the external signal frequency. The peak amplitude achieves its maximal value in the regime of stochastic resonance (SR), that can be used for detecting the SR effect.