Международная студенческая научно-практическая конференция «Инновационное развитие государства: проблемы и перспективы глазам молодых ученых». Том 3

Kharchenko N.I., Zaitseva T.A., Osadcha O.V.

Oles Honchar Dnipropetrovsk National University, Ukraine


The tendency of using mathematical methods and calculations has received wide spreading in a variety of social and humanitarian fields. Presently no serious scientific sociological research can be held. The use of computer technologies in information processing is one of the most important aspects of sociological research. The use of mathematical tools for social systems is faced with considerable difficulties, because clarity and certainty of mathematical logic intersects with subjectivity and broad thinking of sociology. Therefore, researchers meet difficult task to apply all the possibilities of modern information technology, mathematical and statistical system, as well as their own mental capacity to build concrete conclusions on the basis of the figures and graphs.

The development of computer hardware and software has enabled a large number of software products for the study of nonlinear dynamical systems – from the simplest applications of modeling and visualization of the dynamics to more complex, engaged in the construction of basins of attraction, the calculation of Lyapunov exponents, bifurcation analysis, all kinds of dimensional characteristics calculations, restoring of attractors by implementations etc.

Modern mathematical packages are convenient means for carrying out mathematical research, development and analysis of algorithms, mathematical modeling and computer experiment. A large number of mathematical modeling packages exists nowadays.

The AnT package is a software package for modeling and analyzing of dynamic systems. It allows you to analyze discrete maps, periodic time of discrete maps, ordinary differential and functional equations in private as well as stochastic systems, hybrid systems and external input data that will be interpreted as a time series. This package implemented the following methods: calculation of Lyapunov exponents, calculation of Poincare sections and return of the card, time and spectral analysis, some general assessment of the trajectory, singular decomposition, the definition of geometric properties of attractive sets, the definition of unstable orbits and some qualitative methods based on symbolic dynamics, as for example, symbolic entropy. Each research method keeps its performance in the data files that can be visualized and evaluated in the end of modeling.

Package for the mathematical modeling IDMC is an integrated, easy and open source program that is designed for modeling and dynamic analysis of nonlinear models. The package was developed as a tool for learning and research, which is very easy to download and use. Numerical calculations are performed on models included in the package, or any model that is formulated by the user, and easily coded. Graphical user interface provides fast generation of graphical data of good quality that can be saved as .png files. The package is based on the Java and C++ languages. Native library of language C idmclib is used. Capabilities of the package: numerical simulation trajectories, the choice of different initial values ​​or parameters, the construction of bifurcation diagrams for the study of boundary sets with respect to one parameter or two-dimensional parameter space, the calculation of Lyapunov exponents in time by a single parameter or two-dimensional parameter space, research basins of attraction, stable and unstable manifolds; absorbing region (some options are only available for cards).

PyDSTool package includes: effective discrete mapping modeling tools, a hybrid model and events of support; bifurcational analysis, interactive command line / script interface (no GUI), easy creation of complex models using a hierarchical object-oriented data structures; modular design that allows you to extend the code easily to support other algorithms and data structures, data structures and tools to evaluate options, additional conditions for certain programs, including biomechanical modeling, computational neuroscience and Systems Biology, a lot of examples and documentation.

To construct a mathematical model of analysis and prediction of adaptive processes of today's youth the survey among students of the Faculty of Applied Mathematics,Dnipropetrovsk National University named after O.Honchar was conducted. The survey of students was in the form of questionnaires. The content profiles were, in addition to general questions about age, gender and future career, the questions about the motivates of students to the choice of a profession. In the questionnaire there were questions about the motivation of students to study and questions that help determine the degree of social adaptation and realization of future profession.

Similar research by the same profiles was carried out for three years in a row. Empirical data collected during the survey, do not allow to make correct conclusions, to find patterns and trends, and verify the hypothesis that were made by the program. The resulting primary socio-logical information (answers of respondents, expert assessments, observation, etc.) has to be compiled, analyzed and integrated scientifically.

Among the software tools to apply modern methods of mathematical statistics for processing of data, the statistical data package SPSS was selected. This package was used to hold frequency analysis; to build adjacency tables to identify the relationship between the variables; this relationship was analyzed using correlation analysis and charts and graphs were constructed for clarity.

 Based on previous research and this year's research on the adaptation of students to the profession, statistical relationships and dependencies were found, as well as the comparative analysis was made.

To construct mathematical models of dynamic systems the iDMC 2.0.5 modeling and dynamic analysis package was used. The modeling of dynamic systems was conducted on the basis of bifurcation diagrams, phase trajectories, Lyapunov exponent. During the simulation the evaluations of different parameters of their interaction were obtained; charts and models were constructed, a comparative analysis was made.