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


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Matrosov V. V. Some particularities of dynamical behaviour of two cascade coupled phase locked loops. Izvestiya VUZ. Applied Nonlinear Dynamics, 1997, vol. 5, iss. 6, pp. 52-60. DOI: 10.18500/0869-6632-1997-5-6-52-60

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Russian
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Article
UDC: 
519.673; 621.396.66

Some particularities of dynamical behaviour of two cascade coupled phase locked loops

Autors: 
Matrosov Valerij Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Abstract: 

Results of investigations of dynamic regimes and their bifurcations in the model on phase torus of two cascade coupled phase locked loops are presented.

Key words: 
Acknowledgments: 
The work was carried out with the financial support of the Russian Foundation for Basic Research (projects 94-01-00957, 96-02-16559). The numerical study used computer modeling technology and software created with the financial support of the Ministry of Science and Technical Policy of the Russian Federation (State Scientific and Technical program "Advanced Information Technologies", project 05.06.1172).
Reference: 
  1. Kapranov MV. Cascade frequency phase adjustment system. Dynamics of Systems. 1976;11:76.
  2. Matrosov VV, Korzinova МV. Collective dynamics of cascade connection of phase systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(2):10-16.
  3. Matrosov VV, Shalfeeva МV. Influence of coupling parameters on the nonlinear dynamics of two cascade-coupled phase-locked loops. Radiophys. Quantum Electron. 1995;38(3-4):180-182. DOI: 10.1007/BF01037895.
  4. Matrosov VV, Korzinova МV. Synchronous and auto-oscilling modes of cascade connection of phase systems. In: Rabinovich MI, editor. Bulletin Of Nizhny Novgorod State University. Nonlinear Dynamics - Synchronization and Chaos. Nizhny Novgorod: Nizhny Novgorod University Publishing; 1996. P. 77-92.
  5. Korzinova MV, Matrosov VV. Modeling of nonlinear dynamics of cascade coupling of phase systems. Radiophys. Quantum Electron. 1993;36(6):815-819. (in Russian).
  6. Fedosova TS. Features of bifurcations in the phase automatic frequency adjustment system with a harmonic frequency divider. Radioelectron. Commun. Syst. 1978;21(7):60.
  7. Ponomarenko VP, Matrosov VV. Dynamic properties of a two-circuit interconnected phase synchronization system. Soviet J. Comm. Tech. Electron. 1984;29(6):1125-1133.
  8. Shakhgildyan VV, Belyustina LN. Phase Synchronization Systems. М.: Radio i svyaz; 1975. 288 p. (in Russian).
  9. Anishchenko VS. Complex Oscillations in Simple Systems. М.: Nauka; 1990. 312 p. (in Russian).
  10. Ponomarenko VP‚ Matrosov VV. Automation of research on nonlinear dynamics of synchronization systems. Bulletin of the Upper Volga Branch of the Academy of Technological Sciences of the Russian Federation. High technologies in radio electronics. 1997;2(4):15-21.
  11. Barbashin EA, Tabueva VA. Dynamic Systems with Cylindrical Phase Space. M.: Nauka; 1969. 299 p.
  12. Belykh VN, Verichev NN. Coupled rotor dynamics. Radiophys. Quantum Electron. 1988;31(6):503-512. DOI: 10.1007/BF01044654.
  13. Bautin NN. Behavior of Dynamic Systems near the Boundaries of the Stability Region. М: Nauka; 1984. 164 p.
  14. Pliss VА. Nonlocal Problems of the Theory of Oscillations. N.Y.: Academic Press; 1966. 306 p.
  15. Shilnikov LP. Bifurcation theory and Lorentz model. In: Marsden J, McCraken M. Bifurcation of the Birth of the Cycle and its Applications. М.: Mir; 1980. P. 317-335.
Received: 
29.09.1997
Accepted: 
26.01.1998
Published: 
18.03.1998