General systems theory

Purposeful System, and Subjective Evolution Aspect Systemology
V F. Petrenko, A. P. Suprun

Abstract. In systemology regain the rights of the category objectives. However, studies are limited to mostly closed systems and are the object, although the object does not apply teleological principle. The article discusses the possibilities included in the systematic analysis of the subject and approaches to the study of evolutionary processes in open systems. The problems of the subjective approach in psychosemantics.

Keywords: systemology, teleological principle, subjective and object approach, open systems, evolutionary processes, the mental map, the semantic space.Classification andrewies bordermetrics model.

Classification and rewies bordermetrics model
VV Shumov

Abstract. Due to the increasing cross-border crime (terrorism, drug trafficking, illegal migration, etc.) humanity was faced with new threats in the field of national and homeland security. Understanding the Earth's limited resources has led to the creation of areas with mixed legal status and, consequently, the organization of services the Coast Guard. These factors have caused a sharp increase in scientific papers on decision support in the field of border security with the use of mathematical methods. The article presents an overview of the basic work on bordermetrics.

Keywords: bordermetrics, border safety, border control, game-theoretical model.

The interdisciplinary approach on a basis gomoheterogenica in research of quality of life of city settlements
A. V Potapov

Abstract. In article possibility of application of the gomogenno-heterogeneous approach to studying of qualitative conditions of city development is considered. The conclusion that this approach should be modified elements of evolutionxary and system ap-
proaches for the purpose of a complex and objective estimation of dynamics of city development and its authentic interpretation is drawn.

Keywords: gomoheterogenica, uniformity, heterogeneity, a quality spiral.

Formation of a segment of scientific networks on Runet
M. E. Sokolova

Abstract. The article "Formation of a segment of scientific networks in RuNet" deals with the forming segment of scientific social networks in the last decade in RuNet. It considers different types of research services Web 2.0 (scientific social networks, blogs, search engines, bookmarks, etc.), shows their place in the successive development of the information environment of Russian science, analyzes the trends of their development. The article raises the question about the necessity of state scientific and inormation policy in this area.

Keywords: scientific social networks, research services Web 2.0, scientific communications.

Dynamical systems

Numerical research of transition to turbulence in the problem on two-dimensional current of a viscous compressed spending liquid in the channel with symmetric expansion
N. M. Evstigneev, N. A. Magnitskii, O. I. Ryabkov

Abstract. In the paper numerical analysis of occurrence and transformation of initial perturbations in a problem on a current of viscous compressed spending liquid in the channel with symmetric expansion is considered at small values of the Much number (M<0.2). For modeling current of a liquid the integro-differential Boltzmann equations are used which are decomposed on Knudsen number. For modelling the equations of magnetodynamics the vector analogue of Boltzmann equation is used. Decomposition of system of the integro-differential equations on small parameter gives an approximation of magnetodynamics equations for compressed liquid.

Keywords: viscous compressed liquid, turbulence.

Running waves, impulses and diffusion chaos in excitable mediums
T. V Karamisheva, N. A. Magnitskii

Abstract. It is shown in the present paper that system of partial differential equations such as FitzHugh — Nagumo system with the fixed values of parameters can have infinite number of the various stable wave solutions running along a spatial axis with any speeds, and also running impulses and infinite number of various regimes of spatio-temporal (diffusion) chaos. These solutions are generated by cascades of bifurcations of cycles and singular attractors according to the theory FSM (Feigenbaum—Sharkovskii-Magnitskii) in three-dimensional system of ordinary differential equations in which the system of the FitzHugh—Nagumo equations passes at corresponding automodelling change of variables.

Keywords: excitable mediums, running waves, impulses, diffusion chaos.

Bifurcation diagram of Mathieu— Magnitskii Hamiltonian system
M. A. Korolkova

Abstract. The construction of bifurcation diagram of two-parametrical Hamiltonian system of Mathieu—Magnitskii with two degrees of freedom is carried out in the article.

Keywords: hamiltonian system, dynamical chaos, bifurcation diagram, theory FSM.

Mathematical models of socio-economic processes

Structure of the probabilistic macrosystem demo-economic model (part II)
A. S. Aliev, A. Yu. Popkov, Yu. S. Popkov

Abstract. The structure of the block „Economy" for   the   probabilistic   demo-economic   model   is
created. In the block the principle of entropy maximization is used.

Keywords: macrosystem, entropy model, optimization, spatial economy, production function, GDP.

Complex macroeconomy model
M. G. Zavelsky, D. M. Galin

Abstract. The original macroeconomic model is presented. This model is constructed in offered by authors non-standard way of correct using classical mathematical methods for determination of multi-factorial dependencies on the base of observed data which amount is comparatively small. The model has a hierarchical nature, covers interactions of different markets (commodity, financial, labour), takes territorial non-uniformity of economy and all sorts of controlling influences on it into account, explains regularities which appear herewith. Results of testing model in real circumstances, shown its high short-term prognostic ability under unstable economic conditions, are described.

Keywords: economy of country, short-term development, hierarchical multifactorial statistical macro-models, abstract and theoretically adequate ones, constructing at source information deficit, testing.

System approach to construction of the combined schemes of hypothecary crediting
M. F. Tuboltsev, S. I. Matorin, О. M. Tuboltseva

Abstract. In the work, the technique for construction of effective schemes of hypothecary crediting by association of different financial tools is suggested. Advantages of the combined schemes in comparison with traditional hypothecary crediting are shown.

Keywords: synthesis of systems, functional inquiry, external determinant, financial streams, financial tools, profitableness aggregation, combined financial operation.