Fractional Power Spectra in Diagnostics of controlled Anishchenko-Astakhov System

The article is devoted to the consideration of the diagnostics of the controlled discrete-nonlinear Anishchenko-Astakhov system by the fractional-power spectra of the signals generated by the system. The conditions for the closeness of the system of fractional power-law functions of time, which reduce the errors in the representation of signals of discrete-nonlinear systems by fractional power series, are determined. The peculiarities of the representation of the signals of the discrete-nonlinear Anishchenko-Astakhov system by pulse sequences with expansion in fractional powers of time are revealed, its adequacy in the analysis of system signals is confirmed. Two-dimensional and three-dimensional fractional-power spectra of the signals of the discrete-nonlinear Anishchenko-Astakhov system have been constructed. The ranges of variation of indicators of fractional powers and normalized pulse durations have been determined. The dependence of the structure of fractional power-law spectra of signals of a controlled discrete-nonlinear Anishchenko-Astakhov system, modified by modulation of time sampling parameters, on the modulation depth of control actions, which reduce the correlation intervals of the generated pseudo-random signals, is revealed.