For citation:
Matrosov V. V., Kasatkin D. V. Analysis оf excitation processes оf chaotic oscillations in coupled PLLs . Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 4, pp. 31-43. DOI: 10.18500/0869-6632-2003-11-4-31-43
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Russian
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UDC:
621.391.01
Analysis оf excitation processes оf chaotic oscillations in coupled PLLs
Autors:
Matrosov Valerij Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Kasatkin Dmitry Vladimirovich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract:
The problem of generation оf chaotic modulated oscillations in three elements ensemble of coupled PLLs is discussed. Many types оf transition from regular to chaotic oscillations have been found and illustrated. The influence оf thе coupling оn the chaotic regimes in coupled generators has been analyzed.
Key words:
Acknowledgments:
The work was supported by RFBR (grant 02-02-17573, 03-02-06369), programme "Universities of Russia" (project UR.03.01.027).
Reference:
- Shakhgildyan VB, Lyakhovkin AA. Phase-Locked Loop Systems. Moscow: Svyaz; 1972. 342 p. (in Russian).
- Lindsey WC. Synchronization Systems in Communication and Control. Prentice-Hall; 1972. 695 p.
- Shakhgildyan VV, Belyustina LN, editors. Phase Synchronization Systems. Moscow: Radio I Svyaz; 1982. P. 55 (in Russian).
- Afraimovich VS, Nekorkin VI, Osipov GV, Shalfeev VD. Stability, Structures and Chaos in Nonlinear Synchronization Networks. Gorky: IAP AS USSR; 1989. 256 p. (in Russian).
- Fedosova TS. Analysis of phase synchronization systems with two periodic nonlinearities. Radio Engineering. 1986;33(6):46-48.
- Dmitriev AS, Panas AI, Starkov SO. Dynamic chaos as a paradigm of modern communication systems. Foreign Radio Electronics. Advances in Modern Radio Electronics. 1997;(10):4-26 (in Russian).
- Shalfeev VD, Matrosov VB, Korzinova MB. Dynamic chaos in ensembles of coupled phase systems. Foreign Radio Electronics. Advances in Modern Radio Electronics. 1998;(11):44-56 (in Russian).
- Kapranov MB, Kuleshov BN, Larionova MB, Morozov AG, Udalov NN. Properties of information transmission with manipulation of parameters and initial conditions of chaotic oscillation generators. Foreign Radio Electronics. Advances in Modern Radio Electronics. 2000;(11):48 (in Russian).
- Shalfeev VD, Matrosov VV, Korzinova MV. Chaos in phase systems: Generation and synchronization. In: Chen G, editor. Controlling Chaos and Bifurcations in Engineering Systems. Boca - Raton - London - New York - Washington, D.C: CRC Press; 2000. P. 529.
- Shalfeev VD, Matrosov VB. Chaotically modulated oscillations in coupled phase systems. In: Gaponov-Grekhov AV, Nekorkin VI, editors. Nonlinear Waves 2002. Nizhny Novgorod: IPF RAS; 2003. P. 77 (in Russian).
- Matrosov VB, Kasatkin DV. Dynamic modes of coupled oscillators with phase control. J. Commun. Technol. Electron. 2003;48(5):637-645 (in Russian).
- Matrosov VV. Dynamics of Nonlinear Systems. Software Package for Studying Nonlinear Dynamic Systems With Continuous Time. Nizhny Novgorod: Nizhny Novgorod State University Publishing; 2002 (in Russian).
- Andronov AA, Vitt AA, Khaikin SE. Theory of Oscillators. Dover; 1987. 815 p.
- Belyustina LN, Belykh VN. Qualitative investigation of a dynamical system on a cylinder. Differential Equations. 1973;9(3):403-415 (in Russian).
- Matrosov VV, Shalfeev VD, Forti GL. Regular and Chaotic Oscillations in Pendulum Like Systems. Preprint Dipartamento di matematica «F.Enriques». No. 8. Universita degli studi & Milano; 2000. 17 p.
- Bergé P, Pomeau Y, Vidal C. L'ordre dans le chaos: vers une approche déterministe de la turbulence. Hermann; 1984. 353 p. (in French).
- Schuster HG. Deterministic Chaos. An Introduction. Weinheim: Physik-Verlag; 1984. 220 p.
- Matrosov VB, Korzinova MV. Synchronous and self-oscillatory modes of cascade connection of phase systems. Bulletin of University of Nizhni Novgorod. Nonlinear Dynamics - Synchronization and Chaos. Nizhni Novgorod University Publishing; 1996. P. 77-92 (in Russian).
- Neimark YI, Landa PS. Stochastic and Chaotic Oscillations. Dordrecht: Springer; 1992. 500 p. DOI: 10.1007/978-94-011-2596-3.
- Belykh VN, Verichev NN. Coupled rotor dynamics. Radiophys. Quantum Electron. 1988;31(6):503–512. DOI: 10.1007/BF01044654.
- Kazanovich YB, Borisyuk RM. Study of synchronization 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; 1996. P. 124-150 (in Russian).
Received:
15.02.2003
Accepted:
17.03.2003
Available online:
29.11.2023
Published:
31.12.2003
Journal issue:
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