Scale invariance criteria of dynamical chaos

Authors

  • Z. Zh. Zhanabaev
  • Y. T. Kozhagulov
  • S. A. Khokhlov

Keywords:

information, entropy, fractal, chaos, self-organization.

Abstract

This work is devoted to study out the following question: does any qualitative criteria of realization of such universal phenomena as self-organization exist in open systems? Self-organization is also called the appearance of order from chaos under the conditions ofnon-linearity,non-equilibrium and nonclosure. Information entropy and fractal dimension of a set of physical values are usually used as quantitative characteristics of chaos. The more detailed characteristic of dynamical chaos is the Kolmogorov-Sinay entropy. Inhomogeneity of elements of a phase space can be taken into account by use of this characteristic. Technically, precise calculation of Kolmogorov – Sinayentropy can’t be realized. Uncertain questions are: What is the minimum of increasingof entropy, how muchitdecreases atself-organization? Also it was not ascertained the connection between entropy criterion of selfsimilarity and self-affine with fractal dimensions characterized corresponding chaotic processes. In the paper the values of information at fixed points of probability function of density of information

References

KlimontovichYu.L. Information Conserning
the States of Open Systems // PhysicaScripta.
– 1998. – Vol.58. – P. 549.
2. Slomczynski W., Kwapier J., Zyczkowski
K. Entropy Computing Via Integration over Fractal
Measures // Chaos. – 2000. –№1 (10). –
P. 180-188.
3. Piotronero L., Tosatti E. Fractals in Physics.
–Amsterdam: North Holland. – 1986. – 476 p.
4. ZhanabayevZ.Zh. Kriteriisamopodobia I
samoaffinnostidynamicheskogochaosa // KazNU
Bulletin, Physics series. – 2013. – №1 (44). –
P. 58-66.
5. TsallisC. J. Possible generalization of
Boltzmann-Gibbs statistics // Stat. Phys. – 1988. –
Vol. 52. – P. 479-487.
6. Feder J. Fractals. – N.Y.: Plenum press. –
1988. – 283 p.

Downloads

How to Cite

Zhanabaev, Z. Z., Kozhagulov, Y. T., & Khokhlov, S. A. (2013). Scale invariance criteria of dynamical chaos. International Journal of Mathematics and Physics, 4(2), 29–37. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/74

Issue

Section

Chemical Physics and Radio Phisics