Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University515210.18287/2541-7525-2017-23-2-51-59UnknownTHE MAPPINGS OF VAN DER POL — DYUFFING GENERATOR IN DISCRETE TIMEZaitsevV. V.morenov@ssau.ruShilinA. N.morenov@ssau.ruSamara National Research University2109201723251592109201721092017Copyright © 1970, Zaitsev V.V., Shilin A.N.1970<p>In the work transition to discrete time in the equation of movement of van der Pol Dyuffing generator is described. The transition purposeto create mappings of the generator as subjects of the theory of nonlinear oscillations (nonlinear dynamics) in discrete time. The method of sampling is based on the useof counting of the pulse characteristic of an oscillatory contour as the sampling series for a signal in aself-oscillating ring active nonlinearity the resonator feedback. The choice of the consecutive scheme of excitement of a contour allows to receive the iterated displays in the form of recurrent formulas. Two equivalent forms of discrete displays of the generator of van der Pol Dyuffingcomplex and valid are presented. In approximation of method of slow-changing amplitudes it is confirmed that the created discrete mappings have dynamic properties of an analog prototype. Also within the numerical experiment it is shown that in case of the high power of generation the effect of changing of frequencies of harmonicas of the generated discrete signal significantly influence dynamics of the self-oscillators. In particular, in the discrete generator of van der Pol Dyuffing the chaotic self-oscillations are observed.</p>автоколебательная система, импульсная характеристика, дискретное отображе- ние, метод медленно меняющихся амплитуд, хаотические автоколебания.self-oscillatory system, pulse characteristic, discrete mapping, method of slow-changing amplitudes, chaotic self-oscillations.[[1] Kuznetsov A.P., Kuznetsov S.P., Ryskin N.M. Nelineinye kolebaniia [Nonlinear oscillations]. M.: FIZMATLIT, 2005, 292 p. [in Russian].][[2] Kuznetsov A.P., Seliverstova E.S., Trubetskov D.I., Turukina L.V. Fenomen uravneniia van der Polia [Phenomenon of van der Pol equation]. Izvestiya Vysshikh uchebnykh zavedeniy. Prikladnaya nelineynaya dinamika [Izvestiya VUZ. Applied Nonlinear Dynamics], 2014, Vol. 22, no. 4, pp. 3–42 [in Russian].][[3] Kalyanov E.V., Kislov V.Ya. 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