DOI: https://doi.org/10.15673/2072-9812.1/2014.29271

Геометрия хаоса: Расширенный подход к описанию хаотической динамики в некоторых природных системах

Александр Васильевич Глушков, Василий Владимирович Буяджи, Елена Леонидовна Пономаренко

Аннотация


Представлены новый расширенный подход к описанию хаотической динамики в ряде природных систем, в частности, его численное приложение к описанию динамики гидроэкологических систем. Подход включает комплексное применение усовершенствованного метода средней взаимной информации, алгоритма корреляционного интеграла, анализа на основе показателей Ляпунова и др. методы.

Ключевые слова


геометрия хаоса; нелинейный анализ; природные системы

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Литература


Glushkov A.V., Bunyakova Yu.Ya., Analysis and estimation of anthropogenic loading influence on industrial city air basin.-Odessa: Ecology, 2011.-290P.

Glushkov A.V., Chaos-geometrical universal numerical approach to life science processes: Theoretical basis’s// Computational Life Sciences (Sprinfger), in print.

Glushkov A.V., Khokhlov V.N., Tsenenko I.A. Atmospheric teleconnection patterns: wavelet analysis// Nonlin. Proc.in Geophys.-2004.-V.11,N3.-P.285-293.

Bunyakova Yu.Ya., Glushkov A.V., Fedchuk A.P., Serbov N.G., Svinarenko A.A., Tsenenko I.A., Sensing non-linear chaotic features in dynamics of system of couled autogenerators: standard multifractal analysis// Sensor Electr. and Microsyst. Techn.-2007.-N1.-P.14-17.

Glushkov A.V., Khokhlov V.N., Loboda N.S., Bunyakova Yu.Ya., Short-range forecast of atmospheric pollutants using non-linear prediction method// Atmospheric Environment (Elsevier).-2008.-Vol.42.-P. 7284-7292.

Bunyakova Yu.Ya., Khetselius O.Yu., Non-linear prediction statistical method in forecast of atmospheric pollutants//Proc. of the 8th International Carbon Dioxide Conference.-Jena (Germany).-2009.- P.T2-098.

Glushkov A.V., Khokhlov V.N., Loboda N.S., Khetselius O.Yu., Bunyakova Yu.Ya., Nonlinear prediction method in forecast of air pollutants CO2, CO// Transport and Air Pollution. - Zurich: ETH University Press (Switzerland). -2010. - P.131-136.

Glushkov A.V., Khetselius O.Yu., Bunyakova Yu.Ya., Prepelitsa G.P., Solyanikova E.P., Serga E.N., Non-linear prediction method in short-range forecast of atmospheric pollutants: low-dimensional chaos// Dynamical Systems - Theory and Applications. - Lodz: Lodz Univ. Press (Poland). -2011.- LIF111 (6p.).

Glushkov A.V., Bunyakova Yu.Ya., Zaichko P.A., Geometry of Chaos: Consistent combined approach to treating chaotic dynamics atmospheric pollutants and its forecasting// Proc. of Int. Geometry Center.-2013.-Vol.6,N3.-P.6-14.

Pekarova P., Miklanek P., Konicek A., Pekar J.: Water quality in experimental basins. National Report 1999 of the UNESKO.-Project l.l.-Intern.Water Systems. 1999, 1-98.

KoP-ak K., Saylan L., Sen O., Nonlinear time series prediction of O3 concentration in Cityplacelstanbul.. AtmosphericEnvironment (Elsevier) 34, 2000, 1267-1271.

Kuznetsov S.P., Dunamical chaos.-Moscow: Fizmatlit.-2006.-356P.

Kennel M., Brown R., Abarbanel H., Determining embedding dimension for phase-space reconstruction using a geometrical construction//Phys Rev A.-1992.-Vol.45.-P.3403-3411.

Packard N., Crutchfield J., Farmer J., Shaw R., Geometry from a time series//Phys Rev Lett.-1988.-Vol.45.-P. 712-716.

Grassberger P., SnplaceProcaccia SnI., Measuring the strangeness of strange attractors//Physica D.-1983.-Vol.9.-P.189-208.

Fraser A., Swinney H., Independent coordinates for strange attractors from mutual information// Phys Rev A.-1986.-Vol.33.-P. 1134-1140.

Takens F (1981) Detecting strange attractors in turbulence. In: Rand DA, Young LS (eds) Dynamical systems and turbulence, Warwick 1980. (Lecture notes in mathematics No 898). Springer, Berlin Heidelberg New York, pp 366-381

Mane R (1981) On the dimensions of the compact invariant sets of certain non-linear maps. In: Rand DA, Young LS (eds) Dynamical systems and turbulence, Warwick 1980. (Lecture notes in mathematics No 898). Springer, Berlin Heidelberg N.-Y., p. 230-242

Sano M, Sawada Y (1985) Measurement of the Lyapunov spectrum from a chaotic time series//Phys Rev.Lett.-1995.-Vol.55.-P. 1082-1085

Theiler J., Eubank S., Longtin A., Galdrikian B., Farmer J., Testing for nonlinearity in time series: The method of surrogate data// Physica D.-1992.-Vol.58.-P.77-94.

Kaplan J.L., Yorke J.A., Chaotic behavior of multidimensional difference equations, in: Peitgen H.-O., Walter H.-O. (Eds.), Functional Differential Equations and Approximations of Fixed Points. Lecture Notes in Mathematics No. 730. Springer, Berlin.-1979.-pp.204-227.