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We offer the dissipative stochastic dynamic model of the language sign evolution, satisfying to the principle of the least action, one of fundamental variational principles of the Nature. The model conjectures the Poisson nature of the birth flow of language signs and the exponential distribution of their associative-semantic potential (ASP). The model works with stochastic difference equations of the special type for dissipative processes. The equation for momentary polysemy distribution and frequency-rank distribution drawn from our model do not differs significantly (by Kolmogorov-Smirnov’s test) from empirical distributions, got from main Russian and English explanatory dictionaries as well as frequency dictionaries of them.

This paper presents a universal method for constructing an agent-based model of complex systems for their further clear computer representation by means of object-oriented programming languages. The method specifies both steps of model developing from the mathematical description of the system to the determined architecture of the program simulating the system. The efficiency of the method is illustrated by the construction of the two simulation models for the complex systems of various origins: the interactive simulation of the stock exchange and space-time simulation of biological species competition.

The article discusses the emergence of chaotic attractors in the system of three ordinary differential equations arising in the theory of «reaction-diffusion» systems. The dynamics of the corresponding one- and two-dimensional maps and Lyapunov exponents of such attractors are studied. It is shown that the transition to chaos is in accordance with a non-traditional scenario of repeated birth and disappearance of chaotic regimes, which had been previously studied for one-dimensional maps with a sharp apex and a quadratic minimum. Some characteristic features of the system — zones of bistability and hyperbolicity, the crisis of chaotic attractors — are studied by means of numerical analysis.

This paper presents definition and solution problem of correct conditions on the boundary, separating subdomains for hyperbolic linear equation systems. The solution algorithm is demonstrated by means of an example system of elastodynamic equations for two spatial variables. Stated approach can be easily expanded on systems of first-order linear hyperbolic equations with random number of spatial variables.

A new grid and cloud services simulation for NICA accelerator complex data storage and processing system are described. This system is focused on improving the efficiency of the grid-cloud systems development by using work quality indicators of some real system to design and predict its evolution. For these purpose the simulation program are combined with real monitoring system of the grid-cloud service through a special database. An example of the program usage to simulate a sufficiently general cloud structure, which can be used for more common purposes, is given.

We consider a model of stacked long Josephson junctions (LJJ), which consists of alternating superconducting and dielectric layers. The model takes into account the inductive and capacitive coupling between the neighbor junctions. The model is described by a system of nonlinear partial differential equations with respect to the phase differences and the voltage of LJJ, with appropriate initial and boundary conditions. The numerical solution of this system of equations is based on the use of standard three-point finite-difference formulae for discrete approximations in the space coordinate, and the applying the four-step Runge-Kutta method for solving the Cauchy problem obtained. Designed parallel algorithm is implemented by means of the MPI technology (Message Passing Interface). In the paper, the mathematical formulation of the problem is given, numerical scheme and a method of calculation of the current-voltage characteristics of the LJJ system are described. Two variants of parallel implementation are presented. The influence of inductive and capacitive coupling between junctions on the structure of the current-voltage characteristics is demonstrated. The results of methodical calculations with various parameters of length and number of Josephson junctions in the LJJ stack depending on the number of parallel computing nodes, are presented. The calculations have been performed on multiprocessor clusters HybriLIT and CICC of Multi-Functional Information and Computing Complex (Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna). The numerical results are discussed from the viewpoint of the effectiveness of presented approaches of the LJJ system numerical simulation in parallel. It has been shown that one of parallel algorithms provides the 9 times speedup of calculations.

In this paper, we consider a quartic family of planar vector fields corresponding to a rational Holling system which models the dynamics of the populations of predators and their prey in a given ecological or biomedical system and which is a variation on the classical Lotka–Volterra system. For the latter system, the change of the prey density per unit of time per predator called the response function is proportional to the prey density. This means that there is no saturation of the predator when the amount of available prey is large. However, it is more realistic to consider a nonlinear and bounded response function, and in fact different response functions have been used in the literature to model the predator response. After algebraic transformations, the rational Holling system can be written in the form of a quartic dynamical system. To investigate the character and distribution of the singular points in the phase plane of the quartic system, we use our method the sense of which is to obtain the simplest (well-known) system by vanishing some parameters (usually field rotation parameters) of the original system and then to input these parameters successively one by one studying the dynamics of the singular points (both finite and infinite) in the phase plane. Using the obtained information on singular points and applying our geometric approach to the qualitative analysis, we study the limit cycle bifurcations of the quartic system. To control all of the limit cycle bifurcations, especially, bifurcations of multiple limit cycles, it is necessary to know the properties and combine the effects of all of the rotation parameters. It can be done by means of the Wintner–Perko termination principle stating that the maximal one-parameter family of multiple limit cycles terminates either at a singular point which is typically of the same multiplicity (cyclicity) or on a separatrix cycle which is also typically of the same multiplicity (cyclicity). Applying this principle, we prove that the quartic system (and the corresponding rational Holling system) can have at most two limit cycles surrounding one singular point.

The paper develops a theory of a new so-called two-parametric approach to the random signals' analysis and processing. A mathematical simulation and the task solutions’ comparison have been implemented for the Gauss and Rice statistical models. The applicability of the Rice statistical model is substantiated for the tasks of data and images processing when the signal’s envelope is being analyzed. A technique is developed and theoretically substantiated for solving the task of the noise suppression and initial image reconstruction by means of joint calculation of both statistical parameters — an initial signal’s mean value and noise dispersion — based on the maximum likelihood method within the Rice distribution. The peculiarities of this distribution’s likelihood function and the following from them possibilities of the signal and noise estimation have been analyzed.

This article is dedicated to investigation of the possibility to predict bypass transition by means of an unsophisticated low-Reynolds $k-\varepsilon$ turbulence model. Such a model has been developed at TESIS Ltd. The model is implemented in the FlowVision software suit. The ideas implemented in the model are discussed in the article. The capability of the model to predict bypass transition is demonstrated on well-known test cases T3B, T3A, T3A-.