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


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Ponomarenko V. P. Nonlinear effects in autooscillatory system with frequency-phase control. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 4, pp. 66-84. DOI: 10.18500/0869-6632-2012-20-4-66-84

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Russian
Article type: 
Article
UDC: 
621.391.01

Nonlinear effects in autooscillatory system with frequency-phase control

Autors: 
Ponomarenko Valerij Pavlovich, Institute of Applied Mathematics and Cybernetics. Nizhny Novgorod state University
Abstract: 

Dynamical modes and nonlinear phenomena in the models of oscillatory system with frequency-phase control in the case of periodic nonlinear characteristics of frequency discriminator are investigated. Stability of synchronous mode is analyzed. The existences of a great number various periodic and chaotic nonsynchronous modes are established. Peculiarities of the system dynamics caused by parameters of frequency control loop are considered. The results are presented in the form of one- and two-parameter bifurcation diagrams, phase portraits, Poincare sections and waveforms of attractors. 

Reference: 
  1. Kapranov MV. About the capture bandwidth with phase-locked loop. High School Scientific Report. Ser. «Radio Engineering and Electronics». 1958;2(9):162 (in Russian).
  2. Kaganov VI, Tereshchenko SV. Noise-immunity of the double-loop system of automatic control. J. Commun. Technol. Electron. 2012;57(3):323–328. DOI: 10.1134/S1064226912020040.
  3. Dmitriev AS, Shirokov ME. Choice of generator for a direct chaotic communications system. J. Commun. Technol. Electron. 2004;49(7):840–849 (in Russian).
  4. Dmitriev AS, Kletsov AV, Kuz’min LV. Generation of ultrawideband phase chaos in the decimeter band. J. Commun. Technol. Electron. 2009;54(6):675–684. DOI: 10.1134/S1064226909060096.
  5. Zaulin IA, Ponomarenko VP. Dynamic modes and bifurcation phenomena in nonlinear static synchronization systems. J. Commun. Technol. Electron. 1993;38(5):889–900 (in Russian).
  6. Ponomarenko VP, Zaulin IA. The dynamics of an oscillator controlled by a frequency-locked loop with an inverted discriminator characteristic. J. Commun. Technol. Electron. 1997;42(7):828–835 (in Russian).
  7. Ponomarenko VP. Formation of complex oscillations in an autooscillation system with a nonlinear frequency control circuit. J. Commun. Technol. Electron. 1999;44(5):526–533.
  8. Ponomarenko VP, Matrosov VV. Self-organization of temporal structures in a multiequilibrium self-excited oscillator system with frequency control. Tech. Phys. 1997;42(3):253–259. DOI: 10.1134/1.1258675.
  9. Ponomarenko VP, Matrosov VV. Complex dynamics of an oscillator controlled by a frequency-locked loop with a combined discriminator. J. Commun. Technol. Electron. 1997;42(9):1125–1133 (in Russian).
  10. Matrosov VV, Shalfeev VD. Dynamic Chaos in Phase Systems: Textbook. Second Edition. Nizhny Novgorod: UNN Publishing; 2009. 271 p. (in Russian).
  11. Ponomarenko VP, Tikhonov EA. Dynamics of an oscillator with frequency-phase control with inversion of the characteristics of the frequency discriminator. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(6):75–91 (in Russian).
  12. Ponomarenko VP, Tikhonov EA. Chaotic and regular dynamics of a self-oscillator system with a nonlinear frequency-phase control loop. J. Commun. Technol. Electron. 2004;49(2):205–214 (in Russian).
  13. Matrosov VV. The dynamics of a frequency- and phase-controlled oscillator. Radiophysics and Quantum Electronics. 2004;47(4):297–304. DOI: 10.1023/B:RAQE.0000041235.04436.84.
  14. Matrosov VV. Modeling the dynamics of a phase-locked loop system with first-order filters. Vestnik of Lobachevsky University of Nizhni Novgorod. Ser. «Mathematical Modeling and Control». 2006;2(31):17–28 (in Russian).
  15. Ponomarenko VP. Dynamical regimes in models of autooscillatory systems with frequency and frequency-phase control. Izvestiya VUZ. Applied Nonlinear Dynamics. 2007;15(3):33–51 (in Russian). DOI: 10.18500/0869-6632-2007-15-3-33-51.
  16. Ponomarenko VP. Dynamical regimes and nonlinear phenomena in generator with frequency-phase control. Izvestiya VUZ. Applied Nonlinear Dynamics. 2008;16(6):18–40 (in Russian). DOI: 10.18500/0869-6632-2008-16-6-18-40.
  17. Kaganov VI. Automatic Control Systems in Radio Transmitters. Moscow: Svyaz; 1969. 232 p. (in Russian).
  18. Zaulin IA, Ponomarenko VP. Analysis of dynamic processes in static synchronization systems. Sov. J. Commun. Technol. Electron. 1989;33(1):106–114 (in Russian).
  19. Zaulin IA, Ponomarenko VP. Synchronous and self-oscillating modes in multi-stable systems with phase control. J. Commun. Technol. Electron. 1993;38(4):732–741 (in Russian).
  20. Ponomarenko VP, Shalfeev VD. Nonlinear automatic frequency-phase control system with wide pull-in range. Radiophysics and Quantum Electronics. 1968;11(10–11):944–946. DOI: 10.1007/BF01077378.
  21. Bautin NN, Leontovich EA. Methods and Techniques for the Qualitative Study of Dynamical Systems on a Plane. Moscow: Nauka; 1984. 488 p. (in Russian).
  22. Bautin NN. The Behavior of Dynamical Systems Near the Boundaries of the Stability Region. Moscow: Nauka; 1984. 176 p. (in Russian).
  23. Shilnikov LP, Shilnikov AL, Turaev DV, Chua L. Methods of Qualitative Theory in Nonlinear Dynamics. Part 2. Moscow-Izhevsk: SRC «Regular and Chaotic Dynamics», Institute for Computer Research; 2009. 534 p. (in Russian).
  24. Anishchenko VS. Complex Vibrations in Simple Systems. Moscow: Nauka; 1990. 318 p. (in Russian).
  25. Matrosov VV, editor. Dynamics of Nonlinear Systems. A Software Package for the Study of Nonlinear Dynamic Systems with Continuous Time: Educational-Methodical Development. Nizhni Novgorod: UNN Publishing; 2002. 54 p. (in Russian).
  26. Suykens JAK, Vandewalle J. Generation of n-double scrolls (n = 1, 2, 3, 4, ...). IEEE Transaction on Circuits and Systems I: Fundamental Theory and Applications. 1993;40(11):861–867. DOI: 10.1109/81.251829.
  27. Radwan A, Soliman AM, Elwakil AS. 1-D digitally-controlled multiscroll chaos generator. International Journal of Bifurcation and Chaos. 2007;17(1):227–242. DOI: 10.1142/S0218127407017288.
Received: 
19.07.2012
Accepted: 
19.07.2012
Published: 
31.10.2012
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