Abstract
The possibilities of using pattern recognition methods to study mathematical models with a large number of parameters are discussed. The principal point is to study models by constructing phase and parametric portraits. This allows one to solve problems of predicting the states of the object described by the mathematical model in hand and controlling the object and analyzing and studying problems that follow from the particular content of the model. Examples of three mathematical models are given to illustrate this problem.
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Yu. I. Neimark, I. V. Kotel’nikov, and L. G. Teklina, “Numerical Research of the Dynamic Systems as the Pattern Recognition Problem,” in Proc. 8th Int. Conf. Pattern Recognition and Image Analysis: New Information Technologies (PRIA-9-2008) (Nizhni Novgorod, 2008), pp. 96–99.
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Yurii Isaakovich Neimark was born in 1920. He is a doctor of technical sciences, a professor in Nizhnii Novgorod State University, the honored scientist of the Russian Federation, the winner of scientific A.A. Andronov and N. Wiener awards, a member of the National Russian Committee on Theoretical and Applied Mechanics. His scientific interests include oscillation theory, theory of dynamic systems, control theory, mathematical simulation, and cybernetics. He is the author of ten monographs; five translated into English, Spanish, and Polish; more than 400 publications; and 20 inventions.
Larisa Grigor’evna Teklina was born in 1948 and graduated from Gorkov State University in 1971. She is a Candidate of Sciences (Physics and Mathematics). At present, she is a leading scientist at the Research Institute for Applied Mathematics and Cybernetics of Nizhnii Novgorod State University. She is the author of more than 50 publications in theoretical cybernetics and mathematical simulation.
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Neimark, Y.I., Teklina, L.G. On possibilities of using pattern recognition methods to study mathematical models. Pattern Recognit. Image Anal. 22, 144–149 (2012). https://doi.org/10.1134/S1054661812010282
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DOI: https://doi.org/10.1134/S1054661812010282