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Method of numerical modeling of generators of quasi-harmonic oscillations

Keywords:

V.V. Zaitsev – Ph. D. (Phys.-Math.), Professor, Head of Department of Radiophysics, Samara State Aerospace University named after academician S.P. Korolev (National Research University). E-mail: zaitsev@samsu.ru Ar.V. Karlov – Leading Design Engineer, JSC «Concern «Avtomatika». E-mail: arkarlov@oao-avtomatika.ru


The algorithm of numerical modeling of the Thomson type self-oscillating system based on using the invariance of impulse response of linear resonators in combination with the formulas of the differential transforms of discrete harmonic functions is offered in the article. The general algorithm for modeling of oscillations of the Thomson type self-oscillators is obtained. As an example, consider the use of the proposed method for modeling the fractional oscillator van der Pol, represented by a differential equation of motion, comprising left-sided Liouville derivative. Received a recursive algorithm for fractional Van der Pol oscillators capable of generating self-oscillation in discrete-time with properties of processes occurring in the oscillator in continuous time. It was found that with increasing depth feedback violated assumption about quasi harmony of self-oscillation. Thus, the resulting al-gorithm is no longer adequately reflect the processes in the fractional oscillator Van der Pol, but it is proposed as an independent object of nonlinear dynamics in discrete-time. It is shown that in such a way designed discrete self-oscillatory system demonstrates both regular and chaotic dynamics. Described a computational method is proposed to use in numerical experiments on the time and frequency characteristics of nonlinear resonance systems.
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