Construction of methods for computing recurrence plots in space with a scalar product

Authors

DOI:

https://doi.org/10.15587/1729-4061.2019.169887

Keywords:

recurrence plots, state vector, atmospheric pollution, complex dynamic systems

Abstract

The methods for calculation of recurrence plots in space with a scalar product were developed. They enable examining the properties and features of the vector of states of dynamical systems of various complexity in natural and social spheres. A new scientific result is the development of scientific-methodical apparatus to calculate recurrence plots of vectors of states of systems in metric spaces expanded on the basis of scalar product. Two methods for calculation of recurrence plots for vectors of states of complex dynamic systems, which are highly informative, moderately complex and universal in dimensionality of the studied space of states, were proposed. In practice, the proposed methods can be used to calculate and compare recurrence plots of states of the studied systems in metric spaces of different dimensionality without additional normalizing. The functionality of the proposed methods was verified based on experimental observations of concentrations of formaldehyde, ammonia and carbon monoxide in the atmosphere of an industrial city. It was established that at the values of angular size of the area of 10° and 30°, the proposed method for calculation of recurrence plots is more informative, less complex and invariant relative to dimensionality of the space of states. It was shown that the methods for calculation of recurrence plots in space with scalar product make it possible to use them if there are short-time intervals of the absence of observations. It was experimentally determined that in some cases of parameters, the results of computation of recurrence plots based on the developed methods coincide with the results obtained when using the known methods. This indicates a more general nature of the proposed methods.

Author Biographies

Boris Pospelov, National University of Civil Defence of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

Doctor of Technical Sciences, Professor

Research Center

Vladimir Andronov, National University of Civil Defence of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

Doctor of Technical Sciences, Professor

Research Center

Ruslan Meleshchenko, National University of Civil Defence of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD

Department of Fire and Rescue Training

Yuliya Danchenko, Kharkiv National University of Civil Engineering and Architecture Sumska str., 40, Kharkiv, Ukraine, 61002

PhD, Associate Professor

Department of General Chemistry

Igor Artemenko, Kharkiv National University of Internal Affairs Lva Landau ave., 27, Kharkiv, Ukraine, 61080

Doctor of Law, Associate Professor

Mikhailo Romaniak, Institute of Public Administration of Ukraine Taras Shevchenko National University of Kyiv Volodymyrska str., 60, Kyiv, Ukraine, 01033

PhD

Anastasiia Khmyrova, National University of Civil Defence of Ukraine Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD

Educational and Scientific Production Center

Tetiana Butenko, Scientific-Methodical Center of Educational Institutions in the Sphere of Civil Defence Chernyshevska str., 94, Kharkiv, Ukraine, 61023

PhD, Senior Research

Department of Organization and Coordination of Research Activities

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Published

2019-06-10

How to Cite

Pospelov, B., Andronov, V., Meleshchenko, R., Danchenko, Y., Artemenko, I., Romaniak, M., Khmyrova, A., & Butenko, T. (2019). Construction of methods for computing recurrence plots in space with a scalar product. Eastern-European Journal of Enterprise Technologies, 3(4 (99), 37–44. https://doi.org/10.15587/1729-4061.2019.169887

Issue

Vol. 3 No. 4 (99) (2019): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2019 Boris Pospelov, Vladimir Andronov, Ruslan Meleshchenko, Yuliya Danchenko, Igor Artemenko, Mikhailo Romaniak, Anastasiia Khmyrova, Tetiana Butenko

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