ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Koronovskii A. A. Discrete map - flow system analog. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 1, pp. 122-130. DOI: 10.18500/0869-6632-1998-6-1-122-130

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Language: 
Russian
Heading: 
Journal in the journal
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-1998-6-1-122-130

Discrete map - flow system analog

Autors: 
Koronovskii Aleksei Aleksandrovich, Saratov State University
Abstract: 

This work deals with the one-dimensional two-parametric maр the dynamics of which is very much like the dynamics of radioengineering oscillator described by the system of three differential ordinary equations. It has been shown that the behaviours of the oscillator and of the discrete map agree very closely.

Key words: 
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Reference: 
  1. Pikovsky AS, Rabinovich MI. Stochastic oscillations in dissipative systems. Physica D. 1981;2(1):8-24.DOI: 10.1016/0167-2789(81)90054-3.
  2. Rabinovich MI. Stochastic self-oscillations and turbulence. Phys. Usp. 1978;21(5):443-469. DOI: 10.1070/PU1978v021n05ABEH005555.
  3. Pikovskii AS. On the statistical properties of the simplest model of stochastic self-oscillations. Radiophys. Quantum Electron. 1980;23(7):883-884. (in Russian).
  4. Andryshkevich AV, Kipchatov AA. Chaos and periodicity of a tunnel-diode oscillator. Radiophys. Quantum Electron. 1990;33(4):315-317. DOI: 10.1007/BF01046974.
  5. Andrushkevich AV, Kipchatov AA, Krasichkov LV, Koronovskii AA. The path to chaos in a piecewise linear model of a tunnel diode generator. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(1-2):93-103. (in Russian).
  6. Pikovsky AS, Rabinovich MI. Simple autogenerator with stochastic behavior. Soviet Physics. Doklady. 1978;239(2):301-304.
  7. Kiyashko SV, Pikovskii AS, Rabinovich MI. Radio-band autogenerator with stochastic behavior. Radio Engineering and Electronic Physics. 1980;25:336-343.
  8. Kipchatov AA, Podin SV. Study of the behavior of a non-autonomous relaxation generator in the parameter space. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(4-5):30. (in Russian).
  9. Genot М. Applications оf 1-D mар from Chua’s circuit: а pictorial guide. Journal Circuits Syst. Comp. 1993;3(2):375-409. DOI: 10.1142/S0218126693000241.
  10. Kuznetsov AP, Kuznetsov SP, Sataev IR. Self—similarity and universality in Chua’s circuit via the approximate Chua’s 1-D map. Journal Circuits Syst. Comp. 1993;3(2):431-440. DOI: 10.1142/S0218126693000265.
  11. Bezruchko BP, Prokhorov MD, Zhalnin AU. Мар modelling оf non— autonomous LR—diode circuit complicated behaviour. In: Proc. of the 5th International Specialist Workshop оn Nonlinear Dynamics of Electronic Systems. NDES’97. 26—27 June 1997, Moscow. Russia. P. 431.
  12. Andronov AA, Vitt AA, Haikin SE. Theory of Oscillations. M.: Fizmatgiz 1981. 914 p. (in Russian).
Received: 
29.07.1997
Accepted: 
08.12.1997
Published: 
15.02.1998
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