Informational and entropic criteria of self-similarity of fractals and chaotic signals

  • Z. Zh. Zhanabaev al-Farabi Kazakh National University, Almaty, Kazakhstan
  • Y. T. Kozhagulov al-Farabi Kazakh National University, Almaty, Kazakhstan
  • S. A. Khokhlov al-Farabi Kazakh National University, Almaty, Kazakhstan
  • A. T. Agishev al-Farabi Kazakh National University, Almaty, Kazakhstan
  • D. M. Zhexebay al-Farabi Kazakh National University, Almaty, Kazakhstan

Abstract

 Abstract. Information entropy and fractal dimension of a set of physical values are usually used us quantitative characteristic of chaos. Normalization of entropy is a well-known problem. This work is devoted to develop a method to do this. In the work proposed criteria for self-similarity of information and informational entropy. We have defined normalized values of information (I1 = 0.567) and informational entropy (I2 = 0.806) as fixed points of probability density function of information and informational entropy. Meaning of these values is described as criteria of self-similarity of fractals and chaotic signals with different dimensions. We have shown that self-similarity occurs if normalized informational entropy S belongs to the ranges [0,I1), [I1,I2), [I2,1), that corresponds to topological dimensions from 1 to 3 of quasi-periodic, chaotic, stochastic objects. Validity of these findings has been confirmed by calculation of entropy for hierarchical sets of well-known fractals and nonlinear maps. These criteria can be applied to a wide range of problems, where entropy is used.

 
 


 

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АнглийскийИспанскийИтальянскийКазахскийКитайский ТрадКитайский УпрКорейскийРусскийТурецкийФранцузский
 
АнглийскийИспанскийИтальянскийКазахскийКитайский ТрадКитайский УпрКорейскийРусскийТурецкийФранцузский
 
 
 
 
 


 
 
 
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Published
Jun 25, 2018
How to Cite
ZHANABAEV, Z. Zh. et al. Informational and entropic criteria of self-similarity of fractals and chaotic signals. International Journal of Mathematics and Physics, [S.l.], v. 9, n. 1, p. 90-96, june 2018. ISSN 2409-5508. Available at: <http://ijmph.kaznu.kz/index.php/kaznu/article/view/251>. Date accessed: 21 mar. 2019.