Registration Number
0222U002570,
0119U101053
, R & D reports
Title
Mathematical Models Research of Physical Processes by Methods of Identification and Recurrent Analysis with the Use of Information Technologies
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Head
Belozyorov Vasiliy Ye., Доктор фізико-математичних наук
Registration Date
14-02-2022
Organization
Oles Honchar Dnipro National University
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"The object of research is systems of differential equations, recurrent neural networks and modern software for modeling dynamic processes. The purpose of the work is to develop models and methods for identifying functional dependencies in large data.
Research methods - modern methods of theory of differential equations, recurrent analysis and computational mathematics. The results of the work - developed new numerical methods and algorithms that allow you to solve some problems of financial activities.
Two modeling methods are considered: the method based on recurrent analysis and the method of neural networks. The first method, the method of reconstructing a system of ordinary differential equations, is used if the researcher has only information about the process in the form of one time series or several time series. It requires the detection of hidden information and makes it possible to find parameters that allow you to detect the following data: the space of the time series (parameter m - the dimension of the ZDR system), the delay parameter (τ - to build the attractor of the system under reconstruction). The adequacy of the constructed system and information from time series can also be considered using nonlinear recurrent analysis. The second method is the neural network method. Neural network is a biological term that defines the system of collecting, processing and transmitting information by the brain of a living being. The method of neural networks allows you to design and study models of any environmental processes and predict their further change. With the help of neural network technologies it is possible to establish the time of a sharp change (crisis) of the normal functioning of biological, economic or social systems. This will allow you to develop a strategy to prevent harmful effects that may occur in these systems. Novelty of development - all results obtained in the report are new.
Product Description
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Yehoshkin Danylo I
Bilozyorov Vasyl Yevgenovych
Huk Natalya A.
Zaytsev Vadym H
Zolot'ko Kostyantyn Yevgenovych
Safronova Inga A.
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2022-03-09
