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1 Zeszyty Naukowe. Quality. Production. Improvement

1 2019

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Methods of fractal analysis and phase trajectories for the improvement of identification of complex technical systems

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Chovnyuk Y. V. , Gumenyuk Y. O. , Djachenko L. A. , Ivanov E. A. , Kravchyuk V. T.

Zeszyty Naukowe. Quality. Production. Improvement

2019

tom No. 2 (11)

41--50

The procedure of the qualitative analysis of complex technical systems is discussed. One may use such methods of analysis for time series characterized the functioning of such systems. These time serious aren’t confirmed the hypothesis of trend existence. One may use at this qualitative analysis the methods of nonlinear dynamics and the theory of chaos. The basis for similar researches is Takens’s theorem. The randomness of the studied dynamical system as the model of the complex technical 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 the phase points in the phase space the split attractor is indicated, which gives the chance to speak about its bifurcation.