Poincare reverse times in the interaction of chaotic and stochastic systems
DOI:
https://doi.org/10.15587/1729-4061.2012.5673Keywords:
Chaotic and stochastic systems, chaos-like structures, Poincare reverse timesAbstract
Nowadays there exists an urgent problem of analysis and forecasting of a great number of heterogeneous interacting information flows in complex structures.
Information interactions are of dual nature of impact on the system and its environment. On the one hand, they act as a regulation mechanism, making order in the system structure, decreasing its complexity, and on the other hand, they lead to the cloning of information objects.
In the evolution of an open system the increase of information flows and objects complicates the information component that in turn causes an increase of the chaotic processes, which transfer the system into a state of dynamic chaos.
Reflecting the above analysis of the interaction of chaotic and stochastic systems, it appears that the dynamic chaos like a random process requires a statistical description.
Dynamical systems with complex trajectories can be described in terms of the geometry of limit sets in the phase space, as well as the evolution of the phase trajectories in time. One of the fundamental peculiarities of the temporal dynamics of systems is the so called Poincare reversion. Poincare reversion means that any trajectory, starting from a point will endlessly pass in time as close as possible to the initial state. Such movements in dynamic systems Poincare called the Poisson stability. The examples of such systems are the systems implementing the conditions of the attractorReferences
- Mathematical encyclopedia. M.: 1984, т.4., p.p. 750-751.
- Loskutov A.Y., Problems of nonlinear dynamics II. Rejection of chaos and control of dynamic systems. The bulletin Moscow University. A series 3. Physics. Astronomy. №3. 2001. – p.p. 3-21.
- Sharipov O.V., Determined chaos and accident. http // filosof.historic.ru/books/item/ f00/soo/z0000242T.
- Olemskoy A.I., The theory of stochastic systems with singular multiplicative noise. UFN. Volume 168, №3, 1998. – p.p. 287-321.
- Hadyn N., Luevano J., Mantica G., Vaienty S. Multifractal properties of return time statistics // Phys. Rev. Lett. 2002, vol. 88, p. 224502.
- Mandelbrot B.B., Fractals and Multifractals: Noise, Turbulence and Galaxies, Selects Vol. 1 (Springer - Verlag, New York, 1989); A. Bunde, S. Havlin (Eds), Fractals in Science (Springer, Berlin, 1994).
- Tel T., Fractals, multifractals, and thermodynamics. // Z. Naturforsh. 1988. Vol. 43a, P. 1154; T.C. Halsey, M.H. Jensen, L.P.Kadanoff, I. Procaccia, B.I. Shraiman, Fractal measures and their singularities: the characterization of strange sets. // Phys. Rev. A. 1986. Vol. 33, p. 1141.
- Kolesov A.Y., Rozov N.T., Turbulence chaos. Modern mathematics and its appendices. Т. 64. 2009. – p.p.39-53.
- Vladimirsky E.I., Ismailov B.I., Nonlinear recurrence analysis as mathematical model of control of chaotic processes. Information technologies, 2011, №5, (177). p.p. 42-45.
- Afraimovich V., Ugalde E., Urias J. Fractal Dimensions for Poincare Recurrences. M.- Izhevsk, Institute of Computer Science. 2011.-292 p.
- Selcuk Emiroglu and Yilmaz Uyarogly. Control of Rabinovich chaotic system based an passive control. Scientific Research and Essays, Vol. 5 (21). 2010. - pp. 3298-3305.
- Olemskoy A.I., Borisyuk B.N., Shudo I.A., Multifractal analysis of temporary numbers. // Vistnik SumDU. Ser. «Physics, mathematics, mechanics ». №2, 2008. –p.p.70-81.
- Dyakonov V., Kruglov In. Mathematical expansions
- MATLAB. The special directory. – Sankt-Peterburg: Piter, 2001. – 480p..
- Vladimirsky E.I., Ismailov B.I., Synchronization in control of chaotic systems. // Information technologies, №1 (185), 2012. – p.p.16-19.
- Vladimirsky E.I., Tagiev F.K., Sinergetic approach to formation of integrated dimensions in intellectual information-measuring systems. Information technologies. 2010, №6 (166). – p.p. 62-67.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Едуард Йосипович Владимирський
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
