THE QUALITANIVE FRACTAL ANALYSIS OF LONG TERM TIME SERIES FOR AGRICULTURAL SOILS’ ELECTRICAL CONDUCTIVITY PARAMETERS: METHODS OF NONLINEAR DYNAMICS, THEORY OF CHAOS, PHASE TRAJECTORIES

Oleksandr BROVARETS, Liubov DIACHENKO, Yurii CHOVNIUK

Abstract


The procedure of the qualitative fractal analysis of long term time series for agricultural soils’ electrical conductivity parameters, for which the hypothesis of trend existence isn’t confirmed, with application of the methods of nonlinear dynamics, theory of chaos and phase trajectories, is presented. The real time series characterizing mentioned above electrical conductivity parameters of Ukrainian soils is considered. The basis for similar researches is Taren’s theorem. The randomness of the studied dynamical system given by time realizations is established by means of Lyapunov’s indicator. The state stability is estimated by Hausdorf ’s fractal dimension and the fractality index. Visual evaluation of the time series was carried out by means of the phase trajectory restoration procedure. As a result of the analysis of phase points in the phase space the split attractor is indicated, which gives the chaise to speak about its bifurcation.


Keywords


qualitative fractal analysis, long term, time series, agricultural soils, electrical conductivity, parameters, methods of nonlinear dynamics, theory of chaos, phase trajectories, Lyapunov’s indicator, fractal dimension, fractality index, phase space, attr

References


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