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Methods of nonlinear dynamics and minimax approximation criterion in the analysis of population dynamics

Keywords:

V.A. Krysko - Dr.Sc. (Eng.), Professor, Head of Department of Mathematics and modeling, Saratov State Technical University named after Gagarin Yu.A. Е-mail: tak@sun.ru I.Yu. Vygodchikova - Ph.D. (Phys.-Math.), Associate Professor, Department of Mathematical Economics, Saratov State University named after N.I. Chernyshevskii. Е-mail: irinavigod@yandex.ru I.R. Pleve  Dr.Sc. (Hist.), Professor, Chancellor, Saratov State Technical University after Gagarin Yu.A. Е-mail: rectorat@sstu.ru T.Yu. Yaroshenko - Ph.D. (Eng.), Associate Professor, Department of Mathematics and modeling, Saratov State Technical University named after Gagarin Yu.A. Е-mail: tyyaroshenko@gmail.com


The work is dedicated to continuing the development of new approaches including mathematical and algorithmic support of the presentation toolkits analysis of dynamics of development of the states using a key indicator of population. Studies of population fluctuations are highly relevant in terms of current trends of development as the humanity as a whole and individual countries in particular. Changing population such as the formation of the European Union, which includes most of the European countries with developed economies can identify some general patterns of human population growth as a whole. The paper deals with quantitative analysis of time series over a long time interval. The authors propose a set of complementary and mathematically sound methods for assessment of dynamic trends for the purpose of data compression and prediction of missing values in the sample. Use economic statistics (population). Applied discrete wavelet transform Haar, research mark the first four Lyapunov exponents trained artificial neural network, and the approximation based on PL task Chebyshev. The article continues to develop new approaches, including mathematical and algorithmic support of the presentation toolkits analysis of dynamics of development of the states using a key indicator of population. The analysis of study results achieved possibility of a strong data compression without loss of significant information content (up to three sample values, or, equivalently, two coefficients approximating polynomial) obtained sample as a result of complex analysis, the use of which for a variety of methods gave more successful predictions than the use of the same sample by the same methods.
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