Study of the volt-ampere time series in the case of evaporation of aluminum wire electrolytes

In the general sense, a dynamic system is a mathematical model of the evolution of a real system whose state at any given time is uniquely determined by its initial state. Often, when studying dynamic systems, the main source of information on the behavior of the object under study is a set of values of the observed quantity taken at certain (successive) points in time, the so-called time series. One of the main tasks in analyzing time series is to reconstruct the dynamic system that generated the series. For example, for a locally parameterized surface, Takens reconstructed the behavior of the original dynamic system using Euclidean coordinates (manifold) of integer dimension. The objectives of this study are to estimate the dimension of the attractor of classical dynamic systems described by the Van der Pol, Henon, and logistic model equations, as well as to identify significant parameters of the percolation sensor system during evaporation of aluminum electrolytes by determining the smoothness of the deterministic model of volt-ampere time series. To estimate the attractor dimension of the dynamic system, the principal component method is used, the idea of which is to rotate the coordinate axes in a multidimensional space and select the directions along which the motion mainly develops. The dimensions of the attractor for the Van der Pol, Henon and logistic model equations are determined, which are equal to two, three and two, respectively. The Hurst index of the volt-ampere time series of the percolation46 Р.Д. Муртазина, М.Д. Биткулов, Э.Р. Шайхиев 20 (2025) 1 Многофазные системы sensor during evaporation of aluminum electrolytes is determined, approximately equal to 0.7. Consequently, the values of this time series are strongly correlated. The principal component method also shows that the considered time series is described by two components.