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Abstract
In the paper we go on our work on application of a chaos geometry tools 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 of environmental radioactivity systems. A usually, an approach combines together application of the advanced mutual information scheme, Grrasberger-Procachi algorythm, Lyapunov exponent's analysis etc.
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How to Cite
Glushkov, A., Khetselius, O., & Buyadzhi, V. (2016). Geometry of a Chaos: Advanced computational ap- proach to treating chaotic dynamics of environ- mental radioactivity systems II. Proceedings of the International Geometry Center, 9(1). https://doi.org/10.15673/tmgc.v9i1.86
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References
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2. 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
3. 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.
4. 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.
5. 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.
6. Glushkov A.V., Kuzakon V.M., Buyadzhi V.V., Solyanikova E.P., Geometry of Chaos: Advanced computational approach to treating chaotic dynamics of some hydroecological systems// Proc. Int. Geom. Centre.-2015.-Vol.8,N1.-P.93-99.
7. Glushkov A.V., Kuzakon V.M., Bunyakova Yu.Ya., Buyadzhi V.V., Geometry of Chaos: Advanced computational approach to treating chaotic dynamics of some hydroecological systems II// // Proc. Int. Geom. Centre.-2015.-Vol.8,N2.-P.91-96.
8. 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.
9. 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.).
10. 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.
11. Parovik P.I., Shevtsov B.M.: Modeling a radon transfer process in mediums with a fracral structure // Mathematical Modelling.-2009.-Vol.21,N8.-P.30-36.
12. KoP.ak K., Saylan L., Sen O., Nonlinear time series prediction of O3 concentration in CityplaceIstanbul.. AtmosphericEnvironment (Elsevier) 34, 2000, 1267-1271.
13. Kuznetsov S.P., Dunamical chaos.-Moscow: Fizmatlit.-2006.-356P.
14. 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.
15. Packard N., Crutcfield J., Farmer J., Shaw R., Geometry from a time series//Phys Rev Lett.-1988.-Vol.45.-P.712-716.
16. Grassberger P., SnplaceProcaccia SnI., Measuring the strangeness of strange attractors// Physica D.-1983.-Vol.9.-P.189-208.
17. Fraser A., Swinney H., Independent coordinates for strange attractors from mutual information// Phys Rev A.-1986.-Vol.33.-P.1134-1140.
18. 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
19. 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
20. Sano M, Sawada Y (1985) Measurement of the Lyapunov spectrum from a chaotic time series//Phys Rev.Lett.-1995.-Vol.55.-P.1082-1085
21. 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.
22. 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.
2. 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
3. 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.
4. 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.
5. 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.
6. Glushkov A.V., Kuzakon V.M., Buyadzhi V.V., Solyanikova E.P., Geometry of Chaos: Advanced computational approach to treating chaotic dynamics of some hydroecological systems// Proc. Int. Geom. Centre.-2015.-Vol.8,N1.-P.93-99.
7. Glushkov A.V., Kuzakon V.M., Bunyakova Yu.Ya., Buyadzhi V.V., Geometry of Chaos: Advanced computational approach to treating chaotic dynamics of some hydroecological systems II// // Proc. Int. Geom. Centre.-2015.-Vol.8,N2.-P.91-96.
8. 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.
9. 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.).
10. 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.
11. Parovik P.I., Shevtsov B.M.: Modeling a radon transfer process in mediums with a fracral structure // Mathematical Modelling.-2009.-Vol.21,N8.-P.30-36.
12. KoP.ak K., Saylan L., Sen O., Nonlinear time series prediction of O3 concentration in CityplaceIstanbul.. AtmosphericEnvironment (Elsevier) 34, 2000, 1267-1271.
13. Kuznetsov S.P., Dunamical chaos.-Moscow: Fizmatlit.-2006.-356P.
14. 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.
15. Packard N., Crutcfield J., Farmer J., Shaw R., Geometry from a time series//Phys Rev Lett.-1988.-Vol.45.-P.712-716.
16. Grassberger P., SnplaceProcaccia SnI., Measuring the strangeness of strange attractors// Physica D.-1983.-Vol.9.-P.189-208.
17. Fraser A., Swinney H., Independent coordinates for strange attractors from mutual information// Phys Rev A.-1986.-Vol.33.-P.1134-1140.
18. 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
19. 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
20. Sano M, Sawada Y (1985) Measurement of the Lyapunov spectrum from a chaotic time series//Phys Rev.Lett.-1995.-Vol.55.-P.1082-1085
21. 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.
22. 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.