On the Transfer of a Number of Concepts of Statistical Radiophysics to the Theory of One-dimensional Point Mappings
https://doi.org/10.18255/1818-1015-2018-1-7-17
Abstract
In the article, the possibility of using a bispectrum under the investigation of regular and chaotic behaviour of one-dimensional point mappings is discussed. The effectiveness of the transfer of this concept to nonlinear dynamics was demonstrated by an example of the Feigenbaum mapping. Also in the work, the application of the Kullback-Leibler entropy in the theory of point mappings is considered. It has been shown that this information-like value is able to describe the behaviour of statistical ensembles of one-dimensional mappings. In the framework of this theory some general properties of its behaviour were found out. Constructivity of the Kullback-Leibler entropy in the theory of point mappings was shown by means of its direct calculation for the ”saw tooth” mapping with linear initial probability density. Moreover, for this mapping the denumerable set of initial probability densities hitting into its stationary probability density after a finite number of steps was pointed out.
Keywords
period doubling bifurcation,
discrete Fourier transform,
Frobenius–Perron equation,
B-spline,
partition of unity
Supporting agencies: This work was supported by RFBR, grant No 18-08-01356-a.
About the Authors
Agalar M. Agalarov
Institute of Physics. Kh. I. Amirkhanova of the Dagestan Scientific Center of the Russian Academy of Sciences
Russian Federation
PhD
Russian Federation
PhD
Alexander A. Potapov
Kotelnikov Institute of Radioengineering and Electronics (IRE) of Russian Academy of Sciences;
JiNan University
Russian Federation
Russian Federation
Dr. Ph.-Math. Sc.;
JNU-IRE RAS Joint Laboratory of Information Technology and Fractal Processing of Signals
Alexander E. Rassadin
Nizhny Novgorod Mathematical Society
Russian Federation
Member of the Presidium
Russian Federation
Member of the Presidium
Anton V. Stepanov
Chuvash State Agriculture Academy
Russian Federation
senior tutor
Russian Federation
senior tutor
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Review
For citations:
Agalarov A.M., Potapov A.A., Rassadin A.E., Stepanov A.V. On the Transfer of a Number of Concepts of Statistical Radiophysics to the Theory of One-dimensional Point Mappings. Modeling and Analysis of Information Systems. 2018;25(1):7-17. (In Russ.) https://doi.org/10.18255/1818-1015-2018-1-7-17
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