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

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Ponomarenko V. P. Dynamical regimes and nonlinear phenomena in generator with frequency-phase control. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 6, pp. 18-40. DOI: 10.18500/0869-6632-2008-16-6-18-40

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Dynamical regimes and nonlinear phenomena in generator with frequency-phase control

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

The paper represents the results of numerical study of dynamical regimes and bifurcation transitions in oscillatory system with frequency-phase control. The study was carried out on the base of mathematical model with three degrees or freedom in cylindrical phase space. Rich variety of various attractors of oscillatory and rotatory type corresponding to modulating modes of the system has been detected. Various scenarios of transition from regular dynamical regimes to chaotic ones under variation of the control loops parameters are analyzed. Strong dependence of oscillatory modes on these parameters that allow to control of modulating modes is established.

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  1. Shakhgildyan VV, Lyakhovkin AA. Phase Locking Systems. Moscow: Svyaz; 1972. 448 p. (in Russian).
  2. Khodakovsky VA, Bychkov VG. Optimal synchronization device for high frequency instabilities of the radio channel. Radioelectronics and Communications Systems. 1974;17(4):29 (in Russian).
  3. Dmitriev AS, Panas AI. Dynamic Chaos: New Carriers of Information for Communication Systems. Moscow: Fizmatlit; 2002. 252 p. (in Russian).
  4. Dmitriev AS, Shirokov ME. Choice of generator for a direct chaotic communications system. J. Commun. Technol. Electron. 2004;49(7):840–849 (in Russian).
  5. Matrosov VV. Regular and chaotic oscillations in the phase system. Tech. Phys. Lett. 1996;22(23):4–8 (in Russian).
  6. Ponomarenko VP, Zaulin IA. Dynamics of an oscillator controlled by a frequency-locked loop with an inverted discriminator characteristic. J. Commun. Technol. Electron. 1997;42(7):828 (in Russian).
  7. Ponomarenko VP. Modeling the evolution of dynamic modes in an oscillator system with frequency control. Izvestiya VUZ. Applied Nonlinear Dynamics. 1997;5(5):44 (in Russian).
  8. 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.
  9. 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.
  10. 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).
  11. Matrosov VV, Kasatkin DV. Analysis of the processes of excitation of chaotic oscillations in interconnected generators with phase control. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(4–5):31–43 (in Russian).
  12. Matrosov VV, Kasatkin DV. Dynamic operating modes of coupled phase controlled oscillators. J. Commun. Technol. Electron. 2003;48(6):698–706 (in Russian).
  13. 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).
  14. 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).
  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. Kapranov MV. About the capture bandwidth with phase-locked loop. High School Scientific Reports. Ser. «Radio Engineering and Electronics». 1958;2(9):162 (in Russian).
  17. Matrosov VV. Dynamics of Nonlinear Systems. A Software Package for the Study of Nonlinear Dynamic Systems with Continuous Time. Nizhni Novgorod: Lobachevsky University; 2002. 54 p. (in Russian).
  18. Afraimovich VS. Internal bifurcations and crises of attractors. In: Gaponov-Grekhov AV, Rabinovich MI, editors. Nonlinear Waves. Structures and Bifurcations. Moscow: Nauka; 1987. P. 189–213 (in Russian).
  19. Kuznetsov SP. Dynamic Chaos. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
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