For citation:
Ponomarenko V. P., Matrosov V. V. Regimes of behaviour in the system of coupled oscillators with phase control. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 4, pp. 52-65. DOI: 10.18500/0869-6632-2000-8-4-52-65
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Article
UDC:
621.391.01
Regimes of behaviour in the system of coupled oscillators with phase control
Autors:
Ponomarenko Valerij Pavlovich, Institute of Applied Mathematics and Cybernetics. Nizhny Novgorod state University
Matrosov Valerij Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Abstract:
The dynamical system on phase torus is considered which describe the behaviour of the coupled phase locked loops. Possible regimes of the system’s behaviour depending on initial frequency mismatch, control circuit coefficients of amplification and coupling extent through controlling signal are investigated. Evaluations of capture range are obtained.
Key words:
Acknowledgments:
The work was supported by the program "Universities of Russia" (project 03.01.33) and RFBR (project 99-02-17742).
Reference:
- Ponomarenko VP. On theory of cross-linked synchronisation systems. Radiophysics and Quantum Electronics. 1971;14(11):1728-1740. (in Russian).
- Ponomarenko VP, Matrosov VV. Dynamic properties of a two-circuit interconnected phase synchronisation system. Radio Engineering and Electronic Physics. 1984;29(6):1125-1133. (in Russian).
- Ponomarenko VP, Matrosov VV. Nonlinear phenomena in the system of interconnected phase synchronisation devices. Journal of Communications Technology and Electronics. 1993;38(4):711-720. (in Russian).
- Ponomarenko VP, Matrosov VV. On the dynamics of the inertial interconnected phase synchronisation system. Journal of Communications Technology and Electronics. 1993;38(4):721-730. (in Russian).
- Ponomarenko VP, Matrosov VV. Complex oscillations in the system of interacting phase-controlled autogenerators. Radiophysics and Quantum Electronics. 1998;41(12):1604-1611. (in Russian).
- Fedosova TS. Analysis of phase synchronisation systems with two periodic nonlinearities. Journal Radioengineering. 1986;6:46-48. (in Russian).
- Lindsey WC. Synchronisation Systems in Communication and Control. New Jersey: Prentice Hall; 1972. 704 p.
- Yuen JH. А double—loop tracking system. IЕЕЕ Trans. оn Commun. 1972;Com.—20(6):1142-1150.
- Ohlson JE. Polarization tracking of a partially coherent signal using a double loop. IЕЕЕ Trans. оn Commun. 1975;Com.—23(9):859-866.
- Kazanovich YaB, Borisyuk RM. Study of synchronisation modes in neural networks of phase oscillators with a central element. In: Shnol EE, editor. Research in mathematical biology. Collection of scientific works dedicated to the memory of A.D.Bazykin. Pushchino: Pushchino Scientific Centre of the Russian Academy of Sciences; 1996. P. 124-150. (in Russian).
- Belykh VN, Verichev NN. About the dynamics of interconnected rotators. Radiophysics and Quantum Electronics. 1988;31(6):688-697. (in Russian).
- Ponomarenko VP, Matrosov VV. Automation of studies of nonlinear dynamics of synchronisation systems. Bulletin of the Upper Volga branch of the INTERNATIONAL ACADEMY OF TECHNOLOGICAL SCIENCES. Ser. High technology in radio electronics. 1997;2(4):15-21.
- Bautin NN, Leontovich EA. Methods and Techniques of Qualitative Study of Dynamic Systems on the Plane. М.: Nauka; 1990. 496 p.
Received:
13.06.2000
Accepted:
24.08.2000
Published:
23.10.2000
Journal issue:
- 249 reads