Scale invariance criteria of dynamical chaos
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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 informationReferences
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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.
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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
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Chemical Physics and Radio Phisics
