Geometry of Chaos: Advanced computational approach to treating chaotic dynamics of some hydroecological systems
DOI:
https://doi.org/10.15673/2072-9812.1/2015.50221Kulcsszavak:
Geometry of chaos, Non-linear analysis, Nature systemAbsztrakt
In the paper we go on our work on application of the chaos theory and non-linear analysis technique to studying chaotic features of different nature systems. Here there are presented the results of using an advanced chaos-geometric approach to treating chaotic dynamics in definiete hydroecological systems. Generally, an approach combines together application of the advanced mutual information scheme, Grrasberger-Procachi algorythm, Lyapunov exponent's analysis etcHivatkozások
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., Buyadzhi V.V., Ponomarenko E.L., Geometry of Chaos: Advanced approach to treating chaotic dynamics in some nature systems// Proc. Int. Geom. Centre.- 2014.-Vol.7,N1.-P.24-29
Glushkov A.V., Kuzakon' V.M., Khetselius O.Yu., Prepelitsa G.P. and Svinarenko A.A., Geometry of Chaos: Theoretical basis's of a consistent combined approach to treating chaotic dynamical systems and their parameters determination// Proc. Int. Geom. Centre.-2013.-Vol.6,N1.-P.6-12.
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., Non-linear 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 1.1.-Intern.Water Systems. 1999, 1-98.
Koзak K., Saylan L., Sen O., Nonlinear time series prediction of O3 concentration in CityplaceIstanbul. Atmospheric Environment}$ (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.