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

For citation:

Kozlov A. K., Shalfeev V. D. Controlling of chaotic oscillations in generator with delayed phase-locked loop. Izvestiya VUZ. Applied Nonlinear Dynamics, 1994, vol. 2, iss. 2, pp. 36-48. DOI: 10.18500/0869-6632-1994-2-2-36-48

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 1994no2p036.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
621.396
DOI: 
10.18500/0869-6632-1994-2-2-36-48

Controlling of chaotic oscillations in generator with delayed phase-locked loop

Autors: 
Kozlov Aleksandr Konstantinovich, Lobachevsky State University of Nizhny Novgorod
Shalfeev Vladimir Dmitrievich, Lobachevsky State University of Nizhny Novgorod
Abstract: 

Problems of excitation of chaotic oscillations in voltage—controlled oscillator with delayed phase—locked loop are considered. Some examples on controlling and use of chaos are presented.

Key words: 
-
Acknowledgments: 
The work was completed with financial support. supported by the Russian Foundation for Basic Research (project 93-02-15424).
Reference: 
  1. Endo T, Chua LO. Synchronization of chaos in phase-locked loops. IEEE Trans. Circuits Syst. 1991;38(12):1580-1588. DOI: 10.1109/31.108517.
  2. Kocarev L, Halle KS, Eckert K, Chua LO, Parlitz U. Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bif. Chaos. 1992;2(3):709-713. DOI: 10.1142/S0218127492000823.
  3. Parlitz U, Chua LO, Kocarev L, Halle KS, Shang A. Transmission of digital signals by chaotic synchronization. Int. J. Bif. Chaos. 1992;2(4):973-977. DOI: 10.1142/S0218127492000562.
  4. Carroll TL, Pecora LM. Synchronizing nonautonomouschaotic circuits. IEEE Trans. Clruits Syst.—II: Analog and Digital Signal Processing. 1993;40(10):646-650. DOI: 10.1109/82.246166.
  5. Cuomo KM, Oppenheim AV. Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett. 1993;71(1):65-68. DOI: 10.1103/PhysRevLett.71.65.
  6. Halle KS, Wu CW, Itoh M, Chua LO. Spread spectrum communication through modulation of chaos. Int. J. Bif. Chaos. 1993;3(2):469-477. DOI: 10.1142/S0218127493000374.
  7. Belskii YuL, Dmitriev AS. Transmission of information through deterministic chaos. J. Comm. Tech. Electron. 1993;38(7):1310-1315.
  8. Volkovskii AR, Rulkov NF. Synchronised chaotic response of a nonlinear oscillatory system as a principle of detecting the information component of chaos. Tech. Phys. Lett. 1993;19(3):71-75.
  9. Kislov VYa. Dynamic chaos and its use in radio electronics to generate, receive and process oscillations and information. J. Comm. Tech. Electron. 1993;38(10):1783-1815.
  10. Kozlov AK, Shalfeeev VD. Selective suppression of deterministic chaotic signals. Tech. Phys. Lett. 1993;19(23):83-86.
  11. Alekseev АА, Kozlov АК, Shalfeev VD. Chaotic mode and synchronous response in a frequency-controlled autogenerator. Izvestiya VUZ. Applied Nonlinear Dynamics. 1994;2(1):71-77.
  12. Andreev YuV, Belskii YuL, Dmitriev АS. Recording and recovery of information using stable cycles of two-dimensional and multidimensional mappings. J. Comm. Tech. Electron. 1994;39(1):114-123.
  13. Ott E, Grebogi C, Yorke JA. Controlling Chaos. Phys. Rev. Lett. 1990;64(11):1196- 1199. DOI:  10.1103/PhysRevLett.64.1196.
  14. Jackson EA. On the control of complex dynamic systems. Physica D. 1991;50(3):341-366. DOI: 10.1016/0167-2789(91)90004-S.
  15. Chen G, Dong X. On feedback control of chaotic nonlinear dynamic systems. Int. J. Bif. Chaos. 1992;2(2):407-411. DOI: 10.1142/S0218127492000392.
  16. Bradley E. Using chaos to broaden the capture range of aphase—locked loop. IEEE Trans. Circuits Syst.—I: Fundamental Theory and Applications. 1993;40(11):808-818. DOI: 10.1109/81.251819.
  17. Genesio R, Tesi A, Villoresi F. A frequency approach for analyzing and controlling chaos in nonlinear circuits. IEEE Trans. Circuits Syst.—I: Fundamental Theory and Applications. 1993;4(11):819-828. DOI: 10.1109/81.251820.
  18. Jonson GA, Hunt ER. Maintaining stability in Chua’s circuit driven into regions of oscillation and chaos. In: Madan RN, editor. Chua’s Circuit: A Paradigm of Chaos. Singapore: World Scientific; 1993. P. 458-462. DOI: 10.1142/9789812798855_0023.
  19. Kapitaniak T, Kocarev L, Chua LO. Controlling chaos without feedback and control signals. Int. J. Bif. Chaos. 1993;3(2):459-468. DOI: 10.1142/S0218127493000362.
  20. Murali K, Lakshmanan M. Chaotic dynamics of the driven Chua’s circuit. IEEE Trans. Circuits Syst.—I: Fundamental Theory and Applications. 1993;40(11):836-840. DOI: 10.1109/81.251823.
  21. Ogorzalek MJ. Taming chaos: Part II-Control. IEEE Trans. Circuits Syst.—I: Fundamental Theory and Applications. 1993;40(11):700-706. DOI: 10.1109/81.246146.
  22. Fujisaka H, Yamada T. Stability theory of synchronized motion in coupled—oscillator systems. Prog. Theor. Phys. 1983;69(1):32-47. DOI: 10.1143/PTP.69.32.
  23. Afraimovich VS, Verichev NN, Rabinovich МI. Stochastic synchronisation of oscillations in dissipative systems. Radiophys. Quantum Electron. 1985;28(9):1050-1060.
  24. Ресоrа LМ, Carroll TL. Synchronization in chaotic systems. Phys. Rev. Lett. 1990;64(8):821-824. DOI: 10.1103/PhysRevLett.64.821.
  25. Farmer JD. Chaotic attractors of an infinite—dimensional dynamical system. Physica D. 1982;4(3):366-393. DOI: 10.1016/0167-2789(82)90042-2.
  26. Hale JK. Theory of Functional Differential Equations. N.Y.: Springer; 1977. DOI: 10.1007/978-1-4612-9892-2.
  27. Afanasyeva VV. On the features of the chaotic dynamics of two symmetrical auto-oscillation systems (non-autonomous Duffing oscillator and autogenerator with late feedback). Tech. Phys. Lett. 1993;19(6):62-66.
  28. Kalyanov EV, Kislov AV. Bifurcations in the generator with delay, stimulated by external influence. J. Comm. Tech. Electron. 1993;38(9):1619.
  29. Ueda Y, Ohta H. Strange attractors in a system described by nonlinear differential—difference equation. In: Kuramoto Y, editor. Proc. 6th Kyoto Summer Inst. Chaos and Statistical Methods. 12-15 September, 1983, Kyoto, Japan. Tokyo: Springer; 1984. Р. 161-166. DOI: 10.1007/978-3-642-69559-9_21.
  30. Belyustina LN, Fishman LZ. About auto-oscillations in the system of phase automatic frequency adjustment with delay. In: Interuniversity Collection Dynamics of Systems: Numerical Methods of Research of Dynamic Systems. Gorky: Gorky University Publishing; 1982. P. 152.
  31. Belyustina LN, Kinyapina MS, Fishman LZ. Dynamics of the phase synchronisation system with delay. Theoretical Electrical Engineering.1990;48:72.
  32. Dvornikov AA, Kapranov МV, Kuleshov VN, Udalov NN. Interrelated spatially distributed phase synchronisation systems. In: Scientific and Technical Conference: Improving the Quality and Efficiency of Synchronisation Devices in Communication Systems. 25—27 May, 1993. Yaroslavl, Russia. 1993. P. 5.
  33. Shakhgildyan VV, Lyakhovkin AA. Phase Auto-tuning Systems. М.: Svyaz; 1972. 224 p. (in Russian).
  34. Shakhgildyan VV, Belyustina LN. Phase Synchronization Systems. М.: Radio i svyaz; 1975. 288 p. (in Russian).
  35. 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.
  36. Belyustina LN, Kozlov АК, Fraiman LА. Stationary processes in a nonlinear non-autonomous SRS with delay. In: Scientific and Technical Conference: Improving the Quality and Efficiency of Synchronisation Devices in Communication Systems. 25—27 May, 1993. Yaroslavl, Russia. P. 52.
  37. Horsthemke W, Lefever R. Noise-Induced Transitions. Theory and Applications in Physics, Chemistry, and Biology. Berlin: Springer; 1984. 322 p. DOI: 10.1007/3-540-36852-3.
Received: 
29.04.1994
Accepted: 
12.06.1994
Published: 
08.08.1994
  • 1650 reads